bml1105 wrote:Ok, but for the original question, we were able to do 1/2 x 1/2 x 1/2 = 1/8 which is the correct answer.
In the question I posted, if I do 1/2 x 1/2 x 1/2 x 1/2, I get 1/16, but that is not the correct answer.
Why is there a difference?
The answer to the original problem is 1/4, not 1/8.
In each problem, we have to account for the NUMBER OF WAYS to get a favorable outcome.
Original problem:
The probability of having a girl is identical to the probability of having a boy. In a family with three children, what is the probability that all the children are of the same gender?
a) 1/8.
b) 1/6.
c) 1/3.
d) 1/5.
e) 1/4.
One way to get a favorable outcome is BBB.
P(BBB) = 1/2 * 1/2 * 1/2.
But a favorable outcome can be achieved in the following ways:
BBB
GGG
Since there a total of 2 ways, we multiply by 2:
(1/2 * 1/2 * 1/2) * 2 = 1/4.
The correct answer is
E.
Your problem:
A couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?
(A) 3/8
(B) 1/4
(C) 3/16
(D) 1/8
(E) 1/16
One way to get a favorable outcome is BBGG.
P(BBGG) = 1/2 * 1/2 * 1/2 * 1/2.
But a favorable outcome can be achieved in the following ways:
BBGG
BGBG
BGGB
GBBG
GBGB
GGBB
Since there a total of 6 ways, we multiply by 6:
(1/2 * 1/2 * 1/2 * 1/2) * 6 = 3/8.
The correct answer is
A.
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