If a couple were planning to have three children, the sample space summarizing the gender outcomes would be: bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg. a. Construct a similar sample space for the possible gender outcomes (using b for boy and g for girl) of two children. b. Assuming that the outcomes listed in part (a) were equally likely, find the probability of getting two girl children. c. Find the probability of getting exactly one boy child and one girl child.

(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, b.

A girl child is denoted by, g.

(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 S 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.

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step-by-step explanation: