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.
Accepted Solution
A:
Answer:a.S={hh,sh,hs,ss}b.tex]\frac{1}{4}[/tex]c.[tex]\frac{1}{2}[/tex]Step-by-step explanation:We are given that a sample space of three childrenS={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 childrenS={hh,sh,hs,ss}b.Number of cases favorable to two healthy children=1Total number of cases=4Number of cases for two healthy children=1Probability =Number of favorable cases divided by total number of casesProbability=[tex]\frac{1}{4}[/tex]Hence, the probability of getting two healthy children=[tex]\frac{1}{4}[/tex]c.We have to find the probability of getting exactly one healthy child and one sick childNumber of cases of one healthy child and one sick child={hs,sh}=2Probability=[tex]\frac{2}{4}=\frac{1}{2}[/tex]Hence, the probability of getting exactly one healthy child and one sick child=[tex]\frac{1}{2}[/tex]