A family has 2 children. Assuming that the sex of a child is independent of anot

Question

A family has 2 children. Assuming that the sex of a child is independent of another child, and that male and female children are equally likely, calculate the following probabilities. Give all answers rounded to two places past decimal. a) What is the probability that both children are girls? Submit Answer Tries o/2 b) What is the probability that at least one of the children is female? Submit Answer Tries 0/2 c) What is the probability that both children are girls if you know that there is at least one daughter? Submit Anewer T Tries 0/2

Explanation / Answer

a) Both are girls:

P = 1/2 * 1/2 = 0.25

b) At least one female:

P = 1 - no female

P = 1 - 1/4 = 0.75

c)

In a family with 2 children there are four possibilities:

1) the first child is a boy and the second child is a boy (bb)

2) the first child is a boy and the second child is a girl (bg)

3) the first child is a girl and the second child is a boy (gb)

4) the first child is a girl and the second child is a girl (gg)

Since we are given that at least one child is a girl there are three possibilities: bg, gb, or gg. Out of those three possibilities the only one with two girls is gg. Hence the probability is 1/3

B) •No., not independent

P(HA) =.2n=P(H)P(A) =.3(.4) =.12

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