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Answer:
(a) The sample space is: S = {bb, bg, gb, gg}
(b) The probability that the couple has two girl children is 0.25.
(c) The probability that the couple has exactly 1 boy and 1 girl child is 0.50.
Step-by-step explanation:
A boy child is denoted by, <em>b</em>.
A girl child is denoted by, <em>g</em>.
(a)
A couple has two children.
The sample space for the possible gender of the two children are:
The couple can have two boys, two girls or 1 boy and 1 girl.
So the sample space is:
S = {bb, bg, gb, gg}
(b)
It is provided that the outcomes of the sample space <em>S</em> are equally likely, i.e. each outcome has the same probability of success.
Compute the probability that the couple has two girl children as follows:
P (2 Girls) = Favorable no. of outcomes ÷ Total no. of outcomes
Thus, the probability that the couple has two girl children is 0.25.
(c)
Compute the probability that the couple has exactly 1 boy and 1 girl child as follows:
P (1 boy & 1 girl) = Favorable no. of outcomes ÷ Total no. of outcomes
Thus, the probability that the couple has exactly 1 boy and 1 girl child is 0.50.