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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri
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25 Jul 2019, 08:00
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80% (01:23) correct 20% (01:32) wrong based on 200 sessions
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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. \(\frac{7}{20}\)
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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri
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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
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Updated on: 25 Jul 2019, 23:37
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) 10075=25 or 25/100 or 1/4
A.3/20
B.1/5
C.1/4
D.3/10
E.7/20



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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri
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25 Jul 2019, 08:23
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
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25 Jul 2019, 08:24
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
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25 Jul 2019, 08:28
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
Answer = C



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In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri
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Updated on: 26 Jul 2019, 00:51
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 = \(\frac{25}{100}\) = \(\frac{1}{4}\)
Answer C
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
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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
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25 Jul 2019, 08:35
IMO answer is C:
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
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25 Jul 2019, 08:38
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
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Updated on: 25 Jul 2019, 11:07
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=6010+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.
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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri
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25 Jul 2019, 08:42
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=100252015105=25
So probability=25/100 =1/4
Hence Answer is C



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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri
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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
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25 Jul 2019, 08:53
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=10075=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
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25 Jul 2019, 08:56
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+MTC  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 = 553*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
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Updated on: 25 Jul 2019, 09:32
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: [3overlapping 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 Answer (C).
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
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25 Jul 2019, 09:09
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 \(\frac{25}{100} = \frac{1}{4}\) Answer: C



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Re: In a group of 100, 25 drink only tea, 20 drink only coffee, and 15 dri
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25 Jul 2019, 09:25
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
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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
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25 Jul 2019, 09:29
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&ta drink all three = t&c&m= a=10 drink only t & c = y = t&c a drink only c&m = z = c&ma
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 = 10075 = 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
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