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Joined: 23 Jan 2021
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Concentration: , International Business
20 boys and 40 girls are in Group A, while at least 7 boys, together w
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27 Jun 2021, 07:55
27 Jun 2021, 07:55
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Question Stats:
65% (02:34) correct
34% (02:55) wrong based on 26 sessions
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20 boys and 40 girls are in Group A, while at least 7 boys, together with some girls are in Group B. To choose one person from each of the group, the probability that both are boys is no greater than 1/15. Which of the following statements must be true?
Indicate all such statements.
A. The number of people in group B is greater than 34.
B. The number of girls in group B is greater than 32.
C. The number of girl in group B is less than 34.
Post a detailed solution and get a kudos!
Indicate all such statements.
A. The number of people in group B is greater than 34.
B. The number of girls in group B is greater than 32.
C. The number of girl in group B is less than 34.
Post a detailed solution and get a kudos!
Re: 20 boys and 40 girls are in Group A, while at least 7 boys, together w
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28 Jun 2021, 00:17
28 Jun 2021, 00:17
3
For group A the probability of picking one boy is 20/60= 1/3
So, the probability of picking one boy from group B will at least 1/5 ( hence, 1/5 * 1/3 = 1/15)
group B has at least 7 boys. So group B must have at least 5*7= 35 person total
So, option A must be true.
option B is false for total 35 person, though it can be true if total person in increased. As it's partially true, we can't take it.
Same goes for option C
So, answer is "A"
Kudos!!!
So, the probability of picking one boy from group B will at least 1/5 ( hence, 1/5 * 1/3 = 1/15)
group B has at least 7 boys. So group B must have at least 5*7= 35 person total
So, option A must be true.
option B is false for total 35 person, though it can be true if total person in increased. As it's partially true, we can't take it.
Same goes for option C
So, answer is "A"
Kudos!!!
20 boys and 40 girls are in Group A, while at least 7 boys, together w
[#permalink]
28 Jun 2021, 01:46
28 Jun 2021, 01:46
2
Lets presume x number of girls (at least) in group B
Now, Probability of picking 1 boy from
Group A= 20/60=1/3
Group B= 7/(x+7)
So, Probabilitt of picking 2 boy from group A & B is
1/3×7/(x+7)=1/15
=> 7/(3x+21)=1/15
=> 3x+21=105
=> x=28
That means in group B the number of girls is 28 or higher.
So, the number of people in group B is (28+7)=35 or more.
Statement A:True.
Statement B:False; Girls# in B can be less than 32
Statement C:False; Girls# in B can be higher than 34
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Now, Probability of picking 1 boy from
Group A= 20/60=1/3
Group B= 7/(x+7)
So, Probabilitt of picking 2 boy from group A & B is
1/3×7/(x+7)=1/15
=> 7/(3x+21)=1/15
=> 3x+21=105
=> x=28
That means in group B the number of girls is 28 or higher.
So, the number of people in group B is (28+7)=35 or more.
Statement A:True.
Statement B:False; Girls# in B can be less than 32
Statement C:False; Girls# in B can be higher than 34
Posted from my mobile device
