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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 health outcomes​ (using h for healthy and s for sick​) of two children.
b. assuming that the outcomes listed in part​ (a) were equally​ likely, find the probability of getting two healthy children.
c. find the probability of getting exactly one healthy child and one sick child.

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Solution:

we havebeen asked to write

a. construct a similar sample space for the possible health outcomes​ (using h for healthy and s for sick​) of two children.

Sample space
=\left \{HH, HS,SH,SS\right \}

Where S=Sick, H=Healthy

b. assuming that the outcomes listed in part​ (a) were equally​ likely, find the probability of getting two healthy children.

From the sample sapce its clear that

Total number of outcomes
=4 (
\left \{HH, HS,SH,SS\right \})

Favourable Outcome
=1 (
{HH})

Hence the Probability
=(1)/(4)\\

c. find the probability of getting exactly one healthy child and one sick child.

From the sample space in part a, its clear that

Total number of possible out come
=4 (
\left \{HH, HS,SH,SS\right \})

Favourable outcome
=2 (
{ HS,SH})

Hence the Probability
=(2)/(4)=(1)/(2)\\

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