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. a. What is the sample​ space?

Answer 1

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

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

c.
`(1)/(2)`

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=
`(1)/(4)`

Hence, the probability of getting two healthy children=
`(1)/(4)`

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=
`(2)/(4)=(1)/(2)`

Hence, the probability of getting exactly one healthy child and one sick child=
`(1)/(2)`