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Shkiper50 [21]
2 years ago
11

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.
Mathematics
1 answer:
marusya05 [52]2 years ago
7 0

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

                =\frac{1}{4} \\=0.25

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

                          =\frac{2}{4} \\=0.50

Thus, the probability that the couple has exactly 1 boy and 1 girl child is 0.50.

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