Question

Given that for simplicity that the number of children in a family is 1, 2, 3, or 4, with probability 1/4 each. Little Joe (a boy) has no brothers. What is the probability that he is an only child? (Set the problem up carefully. Remember to define the sample space, and any events that you use!)

Answer 1

Answer: $\dfrac{1}{4}$

Step-by-step explanation:

Given : The number of children in a family is 1, 2, 3, or 4.

Little Joe (a boy) has no brothers. But he may have sisters.

The sample space for the number of child in Joe's family : {B, BG, BGG, BGGG}, where G represents girl and B represents boys.

Then , for the probability that he is an only child, favorable outcome = B

Thus, the probability that he is an only child is given by :-

$=\dfrac{\text{Favorable outcome}}{\text{Total outcomes}}=\dfrac{1}{4}$

Hence, the probability that he is an only child = $\dfrac{1}{4}$