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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apocritia apocritia · Answer 1 · 2018-09-08T14:05:22+02:00

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[tex]=\left \{HH, HS,SH,SS\right \}[/tex]

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[tex]=4[/tex] ([tex]\left \{HH, HS,SH,SS\right \}[/tex])

Favourable Outcome[tex]=1[/tex] ([tex] {HH}[/tex])

Hence the Probability[tex]=\frac{1}{4}\\[/tex]

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 [tex]=4[/tex] ([tex] \left \{HH, HS,SH,SS\right \}[/tex])

Favourable outcome[tex]=2[/tex] ([tex] { HS,SH}[/tex])

Hence the Probability[tex]=\frac{2}{4}=\frac{1}{2}\\[/tex]