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# In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri

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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:00
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

A. $$\frac{3}{20}$$

B. $$\frac{1}{5}$$

C. $$\frac{1}{4}$$

D. $$\frac{3}{10}$$

E. $$\frac{7}{20}$$

 This question was provided by Experts Global for the Game of Timers Competition

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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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Updated on: 27 Jul 2019, 04:49
Quote:
In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

A. 3/20

B. 1/5

C. 1/4

D. 3/10

E. 7/20

Total=100
Only tea+coffee+mocha=60
Only All three=10
None=5
Only 2 drinks=x

Therefore, 100=60+x+10+5
x=25

Probability=25/100=1/4
Hence C
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Originally posted by kitipriyanka on 25 Jul 2019, 08:05.
Last edited by kitipriyanka on 27 Jul 2019, 04:49, edited 2 times in total.
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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Updated on: 25 Jul 2019, 23:37
1
IMO C

In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

Sol:

The number of people who drink exactly 2 drinks=100(total)-25(only tea)-20(only coffee)-15(only mocha)-5(nothing)-10(all three)
100-75=25 or 25/100 or 1/4

A.3/20

B.1/5

C.1/4

D.3/10

E.7/20

Originally posted by abhishekdadarwal2009 on 25 Jul 2019, 08:22.
Last edited by abhishekdadarwal2009 on 25 Jul 2019, 23:37, edited 1 time in total.
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:23
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

A. 3/20

B. 1/5

C. 1/4

D. 3/10

E. 7/20

Please see solution in the image below

IMO C
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:24
1
Formula: Total = '0' category + '1' category + '2' category + '3' category

--> 100 = 5 + (25 + 20 + 15) + '2' category + (10)
--> 100 = 75 + '2' category
--> '2' category = 25

So, Probability that a member chosen randomly drinks exactly two of the three drinks = 25/100 = 1/4

IMO Option C

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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:28
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

A. 3/20

B. 1/5

C. 1/4

D. 3/10

E. 7/20

Total 100 people = (only tea) + (only coffee) + (only mocha) + (none of three) + (all of three) + (exactly 2 of the drinks)
We are given all the numbers in above equation except exactly 2 of the drinks.
Substituting the numbers we get people have exactly 2 drinks = 100 - 25 -20 -15 - 10 - 5 = 25

So probability of a member chosen randomly drinks exactly two of the three drinks = 25/100 = 1/4

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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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Updated on: 26 Jul 2019, 00:51
1
Total = 100
Sample Space = 100 - 5 = 95

Let, I = People who drink: Only T + Only C + Only M = 25 + 20 + 15 = 60
Let, III = People who drink All (T.C.M) = 10

Therefore, II = People who drink only two of three (TC + CM + MT) = 95 - (60 + 10) = 25

Hence, required Probability = $$\frac{25}{100}$$ = $$\frac{1}{4}$$

Originally posted by Sayon on 25 Jul 2019, 08:30.
Last edited by Sayon on 26 Jul 2019, 00:51, edited 1 time in total.
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:31
If we draw a venn diagram exactly 25 people drinks exactly two drinks.
So, Probability: 25/100 = 1/4
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:35
1

total = only T + only C + only M + (any two) + all three + none

100 = 25+15+10+any two+ 10 + 5

therefore any two = 25

probablity = 25/100 = 1/4
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:38
1
C has to be the answer.
Total is 25+20+15+10+5=75
Hence 25 drink two.
Required probability is 25/100 = 1/4
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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Updated on: 25 Jul 2019, 11:07
1
In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

A. 3/20

B. 1/5

C. 1/4

D. 3/10

E. 7/20

total= a+b+c-(all)-exactly 2 +neither
100=60-10+5
exacty 2= 45
P = 45/60 ; 3/4 ; 1/4
IMO C exactly two of the three drinks
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Originally posted by Archit3110 on 25 Jul 2019, 08:39.
Last edited by Archit3110 on 25 Jul 2019, 11:07, edited 1 time in total.
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:42
1
We can solve it using vein diagram
so we know Only Tea=25
Only Coffee=20 and only mocha=15, 5 none and 10 all three.So if you draw vein you see that all the fields are covered other than those who will drink 2 of the 3 options
therefore the no of people that consume 2 of the 3 drinks=100-25-20-15-10-5=25

So probability=25/100 =1/4

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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:43
In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

To solve this question, all you need is the formula = Total = Group A +B+C -(Exactly) -2(ALL THREE) + Neither. 100 = 45 - exactly

Solving this you will have the number and then Probability is also a formula Favoured/ Total. 35/100 = 7/20

A. 3/20

B. 1/5

C. 1/4

D. 3/10

E. 7/20

IMO E.
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:53
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

Given:
only T=25
only C=20
only M=15
all 3=10
neither =5
Total = 100

using formula Total = exactly 1 + exactly 2+ exactly 3 + neither we can find exactly 2
100=25+20+15+5+10 +exactly 2
exactly 2=100-75=25

To find the probability that a member chosen randomly drinks exactly two of the three drinks we should divide exactly 2/ total

Thus 25/100=1/4

IMO C
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 08:56
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C I think.

We need to calculate number of people who drink exactly two beverages. Assuming, T = tea, C = coffee, and M = mocha

Now, Total = T+C+M -TC - TM - CM + TMC + None
so, 95 = T+C+M-TC - TM - CM+10

We also have, T+C+M - 2*(TC + TM + CM) + 3TMC = 60
so, T+C+M = 2*(TC + TM + CM)+30

Now, 95 = 2*(TC + TM + CM)+30 - (TC + TM + CM)+10
So, TC + TM + CM = 55

People drinking exactly two drinks: TC + TM + CM - 3*TMC = 55-3*10 = 25
So, probability is 25/100 = 1/4
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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Updated on: 25 Jul 2019, 09:32
1
Quote:
In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

A. 3/20
B. 1/5
C. 1/4
D. 3/10
E. 7/20

Rule: [3-overlapping sets] Total=a+b+c+(exactly two)+(exactly three)+neither;
Given: find the probability (exactly two)/(total);

"group of 100" is total = 100
"25 drink only tea, 20 drink only coffee, and 15 drink only mocha" are {a,b,c} = {25,20,15}
"5 drink none of the three" is neither = 5
"10 drink all the three" is exactly three = 10

100=25+20+15+(exactly two)+10+5
(exactly two)=25
(total)=100

Probability: 25/100=1/4

Originally posted by exc4libur on 25 Jul 2019, 09:07.
Last edited by exc4libur on 25 Jul 2019, 09:32, edited 1 time in total.
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 09:09
1
Quote:
In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

We are given:
Total = 100
Drink only tea = 25
Drink only coffee = 20
Drink only mocha = 15
Drink none = 5
Drink all three = 10
We need to find out what is the probability that the chosen person will drink any two drinks.

First, let us identify who will drink any two drinks.
As we have groups of people each drinking only one of the beverages, drinking none, and drinking all three, the remaining people out of 100 will drink any two drinks. $$100 - (25 + 20 + 15 + 5 + 10) = 100 - 75 = 25$$

So, the probability that we chose any of people who drink only two beverages, is $$\frac{25}{100} = \frac{1}{4}$$

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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 09:25
1
Only tea - 25
only coffee - 20
only mocha - 15
all three - 10

total (excluding who drink atleast one) - 95
exactly two = 95 - 25 - 20 - 15 - 10 = 25

Probability = exactly 2 drinks / total population = 25/100 = 1/4

C is correct.
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 09:27
In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?

Total = 100 = only Tea + only Coffee + only mocha + none + all three together
+ any two (coffee and tea together + coffee and mocha together + mocha and Tea together)

Any two = 100 - (25+20+15+5+10) = 25

only 2 or 3drinks = 25+10 = 35

Probability of member who drink 2 or 3 drinks = 35/100 = 7/20 --Option E is the answer
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri  [#permalink]

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25 Jul 2019, 09:29
1
In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 drink only mocha. 5 drink none of the three and 10 drink all the three. What is the probability that a member chosen randomly drinks exactly two of the three drinks?
Solution:
drink none = 5
drink only tea = t = 25
drink only coffee = c = 20
drink only mocha = m = 15
drink only m&t = x=m&t-a
drink all three = t&c&m= a=10
drink only t & c = y = t&c -a
drink only c&m = z = c&m-a

total = 100 = (drink none) + (drink atleast one) = 5 + (t U c U m) = 5 + (t + c + m +x+y+x+a) = 5 + (25+20+15+x+y+z+10) = x+y+z +75
=> drinks exactly two of the three drinks = x+y+z = 100-75 = 25
the probability that a member chosen randomly drinks exactly two of the three drinks = 25/100=1/4

A. 3/20

B. 1/5

C. 1/4 --> correct

D. 3/10

E. 7/20
Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri   [#permalink] 25 Jul 2019, 09:29

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