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. a. what is the sample space?

a.S={hh,sh,hs,ss}

b.tex]\frac{1}{4}[/tex]

c.

Step-by-step explanation:

We are given that a sample space of three children

S={bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg}

a.We have to construct similar space for two children where h for healthy and s for sick.

Then the sample space of two children

S={hh,sh,hs,ss}

b.Number of cases favorable to two healthy children=1

Total number of  cases=4

Number of cases for two healthy children=1

Probability =Number of favorable cases divided  by total number of cases

Probability=

Hence, the probability of getting two healthy children=

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

Number of cases of one healthy child and one sick child={hs,sh}=2

Probability=

Hence, the probability of getting exactly one healthy child and one sick child=

(-5,-28)

i graphed to on desmos.