Question

Find the probability that when a couple has ​children, at least one of them is a . ​(Assume that boys and girls are equally​ likely.)

Answer 1

Answer:

$P(At\ least\ one\ girl) = 0.875$

Step-by-step explanation:

Given

$n = 3$

$B \to boys$

$G \to girls$

$P(G) = P(B) = 0.5$ --- equal probability

See comment for complete question

Required:

$P(At\ least\ one\ girl)$

To do this, we make use of complement rule:

$P(At\ least\ one\ girl) = 1 - P(No\ girl)$

The event that there is no girl out of the 3 children is: B B B

And the probability is:

$P(No\ Girl) = P(B) * P(B) * P(B)$

$P(No\ Girl) = 0.5*0.5*0.5$

$P(No\ Girl) = 0.125$

So:

$P(At\ least\ one\ girl) = 1 - P(No\ girl)$

$P(At\ least\ one\ girl) = 1 - 0.125$

$P(At\ least\ one\ girl) = 0.875$