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]
