Question

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.

Answer 1

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$=\frac{1}{4}$

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$=\frac{2}{4}=\frac{1}{2}$