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# Is the probability of drawing a 3 from a bag of numbered tiles greater

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Math Expert
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Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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07 May 2017, 14:15
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71% (01:06) correct 29% (01:17) wrong based on 223 sessions

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Is the probability of drawing a 3 from a bag of numbered tiles greater than 50%?

(1) There is a 50% probability of drawing any number other than 3 from the bag.
(2) The probability of drawing two threes is 0.

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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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07 May 2017, 20:26
Bunuel wrote:
Is the probability of drawing a 3 from a bag of numbered tiles greater than 50%?

(1) There is a 50% probability of drawing any number other than 3 from the bag.
(2) The probability of drawing two threes is 0.

Hi,

The PROBABILITY will depend on ..
A) number of 3s
B) number of total balls OR
C) ratio of 3s to rest

Let's see the statements...
(1) There is a 50% probability of drawing any number other than 3 from the bag.
This gives us the ratio between 3 and rest..50% so prob=1/2
Also P(3)+P( not 3)=100%.....P(3)+50%=100%......P(3)=50%=1/2

Sufficient

(2) The probability of drawing two threes is 0.
This only means that there is ONLY one 3 in the box
Insufficient

A
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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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07 May 2017, 22:33
Statement 1. Probability of drawing any number other than 3 = 50% which means tiles with number other than 3 constitute 50% of the total tiles. This means tiles with number '3' constitute 100-50 = 50% of the total tiles. So Probability in this case = 50%, which is NOT greater than 50%. The answer is NO.
Hence Sufficient.

Statement 2. If there are say 'n' 3's in the box and total number of tiles is say 'm', then probability of drawing two 3's:
P = n/m * (n-1)/(m-1)
This is given to be zero which means n(n-1) = 0.
n is thus either 0 or 1. So there are either 0 or 1 tiles in the box having number 3

We don't know the total number of tiles in the box. If there are only two total tiles in the box (m=2) then if n=0, probability would be 0 but if n=1, probability would be 50% (still NOT greater than 50%).

If there is a single tile in the box (m=1) then in any case we cannot draw two 3's from the box so probability would be 0 (still NOT greater than 50%).

If there are three tiles (m=3) then if n=0, probability would be 0 but if n=1, probability would be 1/3 or 33.33% (still NOT greater than 50%).

With increasing values of m, probability would keep on decreasing.. But it will always stay less than 50% as you can see.

Hence D
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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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07 May 2017, 22:48
stat1: 50% probability of drawing any number other than 3 from the bag.
50% = 1/2...

implies P(not 3) = 1 - P(3) = 1/2
hence P(3) = 1/2..
suff

stat2 : say only one three exists..no other info..

ans A
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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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22 May 2017, 04:36
And i would like to add:

You can actually make 2 things up from statement 2.
If the chance of two times getting a 3 is 0, then one scenario would be that only one three exists OR no three exists.

Still statement 1 is correct, as you mentioned.
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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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08 Jun 2017, 10:31
chetan2u wrote:
Bunuel wrote:
Is the probability of drawing a 3 from a bag of numbered tiles greater than 50%?

(1) There is a 50% probability of drawing any number other than 3 from the bag.
(2) The probability of drawing two threes is 0.

Hi,

The PROBABILITY will depend on ..
A) number of 3s
B) number of total balls OR
C) ratio of 3s to rest

Let's see the statements...
(1) There is a 50% probability of drawing any number other than 3 from the bag.
This gives us the ratio between 3 and rest..50% so prob=1/2
Also P(3)+P( not 3)=100%.....P(3)+50%=100%......P(3)=50%=1/2

Sufficient

(2) The probability of drawing two threes is 0.
This only means that there is ONLY one 3 in the box
Insufficient

A

Hello Chetan,
How can we say that there is only one three, there may be NIL threes...NO??
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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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25 Jul 2017, 07:05
1 is sufficient. it basically says that drawing a 3 can never be >50% probability.
statement 2 doesn't help at all.

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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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25 Jul 2017, 07:35
1
For Statement 2, it needs to be clear how we're drawing the two tiles - with replacement, or without? If we're drawing with replacement, and the probability of getting two threes is zero, then there are no threes in the bag, so the answer to the question is 'no', and the statement is sufficient.

If we're drawing without replacement, again we may have zero threes in the bag (in which case the answer is 'no'), or we may have exactly one three. But if there's only one three in the bag, and you pick one tile, the probability of picking a three will be 1/n, where n is the total number of tiles. This will only be greater than 50% if n is exactly 1. But the wording of the question (a bag of numbered tiles) suggests that there is more than one tile in the bag. So the pluralization of 'tiles' in the question stem suggests to me that we are meant to rule out the possibility there is only one tile in total, and that would make Statement 2 sufficient also.

But I wouldn't really know how to answer the question, because it's ambiguous whether we should admit the possibility that there is exactly one tile in total in the bag of tiles.
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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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25 Jul 2017, 11:17
I got D

1. The P (drawing 3) + P (not drawing 3) = 1

so we get .5 + x = 1 so x = .5
Therefore the probability of drawing a 3 is not greater than 50% - statement 1 is sufficient

2. It states that the probability of drawing multiple 3's is 0 which indicates that there is only one 3 in the bag. The question prompt describes a "bag of tiles" so we know that there is at least two tiles in the bag. therefore the probability of drawing a 3 is less than or equal to 50%. statement 2 is sufficient
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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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13 Aug 2017, 01:11
Jimbo1912 wrote:
I got D

1. The P (drawing 3) + P (not drawing 3) = 1

so we get .5 + x = 1 so x = .5
Therefore the probability of drawing a 3 is not greater than 50% - statement 1 is sufficient

2. It states that the probability of drawing multiple 3's is 0 which indicates that there is only one 3 in the bag. The question prompt describes a "bag of tiles" so we know that there is at least two tiles in the bag. therefore the probability of drawing a 3 is less than or equal to 50%. statement 2 is sufficient

You got the first statement correct.

The second statement says that the probability of drawing two threes is 0. But we don't know whether there are any tiles numbered 3 or whether there is a single tile with number 3. So, statement 2 is not sufficient.

Hence, Ans A.
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Re: Is the probability of drawing a 3 from a bag of numbered tiles greater  [#permalink]

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22 Aug 2017, 10:40
Bunuel wrote:
Is the probability of drawing a 3 from a bag of numbered tiles greater than 50%?

(1) There is a 50% probability of drawing any number other than 3 from the bag.
(2) The probability of drawing two threes is 0.

(1) Tells us that the probability that a 3 will NOT be drawn from the bag is 50%. Hence the probability that a 3 is drawn from the bag is also 50%
Sufficient

(2) Tells us that there is either one or no 3 in the bag.
Insufficient

Ans A
Re: Is the probability of drawing a 3 from a bag of numbered tiles greater   [#permalink] 22 Aug 2017, 10:40
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