Seven friends, namely Marie, Marlie, Libby, Noah, Harry, David,

Question

Seven friends, namely Marie, Marlie, Libby, Noah, Harry, David, and Thomas, went on a boat riding trip. They formed two groups A and B. Group A had three males and one female, while group B consisted of two females and one male. From each of the two groups, two boat riders were to be selected. What is the probability that two males and two females would be selected?

A. 1/2

B. 4/7

C. 3/5

D. 2/3

E. 5/7

A. 1/2

B. 4/7

C. 3/5

D. 2/3

E. 5/7

paragw · Answer

Case 1: A gives 1M + 1F, B gives 1M + 1F
From A:
P(1M, 1F) = 3/6 = 1/2
From B:
P(1M, 1F) = 2/3
So: (1/2)(2/3) = 1/3

Case 2: A gives 2M, B gives 2F
From A:
P(2M) = 3/6 = 1/2
From B:
P(2F) = 1/3
So: (1/2)(1/3) = 1/6

Hence, 1/3 + 1/6 = 1/2

reruma · Answer

How to do this problem?

MarkGMATMentor · Answer

This probability question has several parts, so break it into steps rather than doing it all at once.

Remember also your fundamental probability rules: AND means multiply, OR means add, and the probability of something NOT happening is equal to 1 minus the probability of it happening.

Group: A:  3 males and 1 female.

There are 2 possibilities: either MM or MF.

To get MM: probability of a male on the first selection = 3/4. Probability of a male on the second selection = 2/3

So, the probability of getting MM (male AND male) is 3/4 * 2/3 = 1/2

Thus the probability of MF is 1 minus the probability of MM, or 1 - 1/2 = 1/2

Group B:  2 females and 1 male.

There are 2 possibilities: either FF or MF.

To get FF: probability of a female on the first selection = 2/3. Probability of a female on the second selection = 1/2

So, the probability of getting FF (female AND female) is 2/3 * 1/2 = 1/3

Thus the probability of MF is 1 minus the probability of FF, or 1 - 1/3 = 2/3

Together: 
Now let's return to the goal: the probability of 2 males and 2 females selected overall. This can happen in two ways: either MM from Group A and FF from Group B, or MF from Group A and MF from Group B.

MM from Group A AND FF from Group B = 1/2 * 1/3 = 1/6

MF from Group A AND MF from Group B = 1/2 * 2/3 = 2/6

So, the probability of either (MM/FF OR MF/MF) is 1/6 + 2/6 = 3/6 = 1/2.  The answer is A.

By breaking a complex probabiliity question like this into separate scenarios and then combining them, a potentially overwhelming problem becomes much more manageable.

Seven friends, namely Marie, Marlie, Libby, Noah, Harry, David,

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Seven friends, namely Marie, Marlie, Libby, Noah, Harry, David,

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