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A randomly selected sample population consists of 60% women  [#permalink]

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A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?

A. 95%
B. 90%
C. 80%
D. 75%
E. 60%

I was able to come up with the double set matrix but could not solve for the probability part. Can you please assist?

Thanks,
Sri

Attachments Matrix.png [ 12.5 KiB | Viewed 19938 times ]

Originally posted by gmattesttaker2 on 01 Jun 2014, 22:44.
Last edited by Bunuel on 02 Jun 2014, 00:10, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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gmattesttaker2 wrote:
A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?

A. 95%
B. 90%
C. 80%
D. 75%
E. 60% According to the matrix the probability of selecting a colorblind person is 0.6 and the probability of NOT selecting a colorblind person is 0.4.

{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.

We are asked to find the approximate probability, so the answer is 95%.

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Re: A randomly selected sample population consists of 60% women  [#permalink]

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gmattesttaker2 wrote:
A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?

A. 95%
B. 90%
C. 80%
D. 75%
E. 60%

I was able to come up with the double set matrix but could not solve for the probability part. Can you please assist?

Thanks,
Sri

To get to the probability part, all you need is the total % of colorblind people.
Say, there are 100 people - 60 women, 40 men.
Out of 60, 90% women are colorblind i.e. 90% of 60 = 54 women
Out of 40, 15% men are colorblind i.e. 15% of 40 = 6 men

Total 60 people of 100 are colorblind.

P(Selecting colorblind person in 3 tries or less) = 1 - P(Selecting a colorblind person in more than 3 tries) = 1 - (40/100)^3 = 117/125 = approx 95%
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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Bunuel wrote:
gmattesttaker2 wrote:
A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?

A. 95%
B. 90%
C. 80%
D. 75%
E. 60% According to the matrix the probability of selecting a colorblind person is 0.6 and the probability of NOT selecting a colorblind person is 0.4.

{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.

We are asked to find the approximate probability, so the answer is 95%.

Doesn't the probability of selection change after the first, second and third?
We are reducing the number of non-color blind people with each try, are we not?
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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ronr34 wrote:
Bunuel wrote:
gmattesttaker2 wrote:
A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?

A. 95%
B. 90%
C. 80%
D. 75%
E. 60% According to the matrix the probability of selecting a colorblind person is 0.6 and the probability of NOT selecting a colorblind person is 0.4.

{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.

We are asked to find the approximate probability, so the answer is 95%.

Doesn't the probability of selection change after the first, second and third?
We are reducing the number of non-color blind people with each try, are we not?

We don't know the size of the sample population so it is not possible to change the probability. Also the word population is used so the assumption is that we select one person, find he is not colorblind, then let him be. We do not remove him from the population. Then we pick another person and check.
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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Bunuel wrote:
gmattesttaker2 wrote:
A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?

A. 95%
B. 90%
C. 80%
D. 75%
E. 60% According to the matrix the probability of selecting a colorblind person is 0.6 and the probability of NOT selecting a colorblind person is 0.4.

{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.

We are asked to find the approximate probability, so the answer is 95%.

Why did you assume that each selection is without replacement?
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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Bunuel wrote:
gmattesttaker2 wrote:
A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?

A. 95%
B. 90%
C. 80%
D. 75%
E. 60%

According to the matrix the probability of selecting a colorblind person is 0.6 and the probability of NOT selecting a colorblind person is 0.4.

{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.

We are asked to find the approximate probability, so the answer is 95%.

It isnt' mentioned any where in the question that they are replaced. How could the probability remain same i.e 0.4 throughout ?
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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rohan567 wrote:

Why did you assume that each selection is without replacement?

As I mentioned above, it is implied in the question. We don't know the size of the sample population so it is not possible to change the probability. Also the word population is used so the assumption is that we select one person, find he is not colorblind, then let him be. We do not remove him from the population. Then we pick another person and check.
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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Hi VeritasPrepKarishma / chetan2u,

I am not able to understand this method-

{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.

_________________________________________

I would have used this method if the question have asked about to find the probability of ATLEAST 3 colorblind person.
Then I first find the probability of of person who NOT colorblind and then subtract it from 1.
_________________________________________

Thanks and Regards,
Prakhar
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Prakhar
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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PrakharGMAT wrote:
Hi VeritasPrepKarishma / chetan2u,

I am not able to understand this method-

{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.

_________________________________________

I would have used this method if the question have asked about to find the probability of ATLEAST 3 colorblind person.
Then I first find the probability of of person who NOT colorblind and then subtract it from 1.
_________________________________________

Thanks and Regards,
Prakhar

Hi PrakharGMAT,

the Q asks us - Prob of choosing a colorblind in not more than 3 choices... OR a colorblind is choosen in any of the three chances....

now 60% are W, 90% are colorblind - so .54 ..
40% are M. 15% are colrblind - .06...
total .54+.06 = 0.6..
so NOT a colorblind = 1-0.6 = 0.4

for this you can do it in two ways,,..

1) take ways in which 1 out of 3 or 2 out of 3 or 3out of three are colorblind- a LONG method
a) 1 out of 3 - .6*.4*.4 *3 = .288
b) 2 out of 3 - .6*.6*.4*3 = .432
c) 3 out of 3 - .6*.6*.6 = .216
add all three .288+.432+.216 = .936
we have multiplied a and b by 3 because in three ways the colorblind or non-colorblind can be choosen - CNN, NCN and NNC

2) the easier way is to find the way wherein NONE of the 3 choosen are colorblind and then subtract that from 1..

so prob that no colorblind is choosen in 3 chances = .4*.4*.4
and prob that atleast one in three is colorblind = 1-none are colorblind = 1-.4*.4*.4 = .936
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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Bunuel wrote:
gmattesttaker2 wrote:
A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?

A. 95%
B. 90%
C. 80%
D. 75%
E. 60% According to the matrix the probability of selecting a colorblind person is 0.6 and the probability of NOT selecting a colorblind person is 0.4.

{The probability of selecting a colorblind person in three tries} = 1 - {the probability of NOT selecting a colorblind person in three tries} = 1 - 0.4*0.4*0.4 = 1 - 0.064 = 0.936 = 93.6%.

We are asked to find the approximate probability, so the answer is 95%.

A question about calculating the {the probability of NOT selecting a colorblind person in three tries}. Isn't this (4/10)*(3/9)*(2/8)=(24/720)=1/30?
1-(1/30)=29/30=96.67%
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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VeritasPrepKarishma wrote:
rohan567 wrote:

Why did you assume that each selection is without replacement?

As I mentioned above, it is implied in the question. We don't know the size of the sample population so it is not possible to change the probability. Also the word population is used so the assumption is that we select one person, find he is not colorblind, then let him be. We do not remove him from the population. Then we pick another person and check.

Hi VeritasPrepKarishma

Because you have said that we don't know the sample size, wouldn't

1 - P(probability of choosing no colorblind in 3 or less tries)

give us

Probability of choosing a colorblind in more than 3 tries + Probability of never choosing a colorblind?
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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I have one doubt .. question says in the experiment scientist will look for a color blind subject until they find one ... It should mean that if he finds on the first turn he would not go for another check .

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Re: A randomly selected sample population consists of 60% women  [#permalink]

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ShashankDave wrote:
VeritasPrepKarishma wrote:
rohan567 wrote:

Why did you assume that each selection is without replacement?

As I mentioned above, it is implied in the question. We don't know the size of the sample population so it is not possible to change the probability. Also the word population is used so the assumption is that we select one person, find he is not colorblind, then let him be. We do not remove him from the population. Then we pick another person and check.

Hi VeritasPrepKarishma

Because you have said that we don't know the sample size, wouldn't

1 - P(probability of choosing no colorblind in 3 or less tries)

give us

Probability of choosing a colorblind in more than 3 tries + Probability of never choosing a colorblind?

We know that "90% of the women and 15% of the men are colorblind".
Eventually, they are bound to pick a colorblind person.
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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vivsleo wrote:
I have one doubt .. question says in the experiment scientist will look for a color blind subject until they find one ... It should mean that if he finds on the first turn he would not go for another check .

Sent from my MotoG3 using GMAT Club Forum mobile app

Yes, that is correct. But instead of calculating all that - get a subject on first try, second try or third try, it is easier to calculate "not get a subject on each of the first three tries."
See the solutions given above.

Note that the answer would be the same.
First try = 60/100
Second try = 40/100 * 60/100
Third try = 40/100 * 40/100 * 60/100

Total = 3/5 + 6/25 + 12/125 = 117/125
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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gmattesttaker2 wrote:
A randomly selected sample population consists of 60% women and 40% men. 90% of the women and 15% of the men are colorblind. For a certain experiment, scientists will select one person at a time until they have a colorblind subject. What is the approximate probability of selecting a colorblind person in no more than three tries?

A. 95%
B. 90%
C. 80%
D. 75%
E. 60%

If the sample population has 60% women and 40% men, and 90% of the women and 15% of the men are colorblind, then the probability that a randomly selected person is colorblind is (0.6)(0.9) + (0.4)(0.15) = 0.54 + 0.06 = 0.6. This also means that the probability that a randomly selected person is not colorblind is 0.4.

We need to determine the probability of selecting a colorblind person in no more than 3 tries.

Let’s calculate the probability for each possible scenario:

Scenario 1: A colorblind person is chosen on the first try.

P(colorblind person is chosen on the first try) = 0.6

Scenario 2: A colorblind person is chosen on the second try. (That is, a non-colorblind person is chosen on the first try.)

P(colorblind person is chosen on the second try) = 0.4 x 0.6 = 0.24

Scenario 3: A color blind person is chosen on the third try. (That is, a non-colorblind person is chosen on each of the first two tries.)

P(colorblind person is chosen on the third try) = 0.4 x 0.4 x 0.6 = 0.096

Thus, the probability of selecting a colorblind person on no more than three tries is 0.6 + 0.24 + 0.096 = 0.936 = 93.6%, which is approximately 95%.

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GMAT 1: 720 Q49 V40 Re: A randomly selected sample population consists of 60% women  [#permalink]

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VeritasPrepKarishma wrote:
rohan567 wrote:

Why did you assume that each selection is without replacement?

As I mentioned above, it is implied in the question. We don't know the size of the sample population so it is not possible to change the probability. Also the word population is used so the assumption is that we select one person, find he is not colorblind, then let him be. We do not remove him from the population. Then we pick another person and check.

Hi Karishma,

As Rohan567 pointed out, we can't replace the selected persons back in to the lot since we know the status of the person once we select them.

So, even if we do without the replacement we will receive the correct answer (but it takes a few more seconds to calculate)

This is how I did it.

From the question we understand that out of total population 60% are colour blind

Hence, by removing the percentage and assuming real numbers we get 60 people out of the 100 are colour blind.

Hence the probability of selecting a colour blind person in the first 3 tries is

= 1- (Probability of not selecting a colour blind person in the first 3 attempts)

= 1- ( 40/100 * 39/99 * 38/98)

=1- (494/8085)

=1-0.06..

=0.94 = 95% (approx)

Ans A
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Re: A randomly selected sample population consists of 60% women  [#permalink]

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Hi All,

There are a couple of different ways to solve this problem. Based on the given info, we have….

60% Women
40% Men

Color-Blind:
90% of Women = (.9)(60%) = 54% of total group
15% of Men = (.15)(40%) = 6% of the total group

NOT Color-Blind = everyone else = 40% of the total group

When it comes to dealing with Probabilities, we can either calculate what we WANT or what we DON'T WANT (and then subtract that result from the number 1 to figure out the probability of what we DO want).

Want + Don't Want = 1

When a probability question gives us multiple tries to accomplish 1 task, it's usually fastest to calculate the probability that we DO NOT accomplish the task, then subtract that from the number 1. Instead of calculating the probability of picking a color-blind person in 3 tries, we'll calculate the probability that we DO NOT select a color-blind person in 3 tries….

Notice the word "approximate"….we can keep things simple….

(NOT)(NOT)(NOT) = (.4)(.4)(.4) = .064 This is the probability of NOT selecting a color-blind person in 3 tries.

The probability of selecting a color-blind person in 3 tries is….

1 - .064 = .936

This is really close to….

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Re: A randomly selected sample population consists of 60% women  [#permalink]

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Now correct me if i am wrong :
here the selection should be without replacement ;
pick a number in your hypothesis to deal with :
60 women
40 men

colorblind women = 60x90%=54
colorblind men = 40x15%=6

a total of 60 color blind people out of 100

probability of selecting a colorblind person in no more than three tries = 1-P(selecting NO colorblind person in the three times) = 1-P(NNN) =
1-(40/100 x 39/99 x 38/98) ( and since we are dealing with proximity) = 1-(40/100)^3 = 0.936 approximately 95%
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A randomly selected sample population consists of 60% women  [#permalink]

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vivsleo wrote:
I have one doubt .. question says in the experiment scientist will look for a color blind subject until they find one ... It should mean that if he finds on the first turn he would not go for another check .

Sent from my MotoG3 using GMAT Club Forum mobile app

Yes, that is correct. But instead of calculating all that - get a subject on first try, second try or third try, it is easier to calculate "not get a subject on each of the first three tries."
See the solutions given above.

Note that the answer would be the same.
First try = 60/100
Second try = 40/100 * 60/100
Third try = 40/100 * 40/100 * 60/100

Total = 3/5 + 6/25 + 12/125 = 117/125

@"VeritasKarishma So it means researcher will try until they dont get colorblind person..It means it is with replacement till they dont get a colorblind?
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