The Solution.
First, we state the probability of developing cancer in a lifetime and that of not developing cancer in a lifetime.
[tex]\begin{gathered} \text{Prob(Cancer) =}0.42 \\ \text{Prob(no cancer}=(1-0.42)=0.58 \end{gathered}[/tex]a. None of the 4 develop cancer:
Possible outcomes=[C'C'C'C']
[tex]\begin{gathered} P(C^{\prime}C^{\prime}C^{\prime}C^{\prime})=pr(C^{\prime})\times Pr(C^{\prime})\times Pr(C\text{)}\times Pr(C^{\prime})=Pr(C^{\prime})^4 \\ \text{Where Pr(C')=probability of not developing cancer.} \\ \text{ =0.58}^4=0.11316\approx0.113(11.3\text{ \%)} \end{gathered}[/tex][tex]\begin{gathered} Pr(C^{}\text{C}C^{}C^{\prime})=Pr(C)\times Pr(C)\times Pr(C)\times Pr(C^{\prime})=Pr(C)^3\times Pr(C^{\prime}) \\ =0.42^3\times0.58=0.0741\times0.58=0.04297\approx0.043\text{ ( 4.3\%)} \end{gathered}[/tex]Therefore, the correct answers are;
a. 0.113 (or 11.3%)
b. 0.043 (or 4.3%)
