Three events A , B and C have probabilities `2/5,1/3a n d1/2` respecively. Given tat `P(AnnC)=1/5a n dP(BnnC)=1/4,` find the values of `P(C//B)a n dP(A^{prime} cap C^{prime})`

Explanation

Here,


`P(A)=frac{2}{5^{prime}} P(B)=frac{1}{3^{prime}} P(C)=frac{1}{2^{3}} P(A cap C)=frac{1}{5} { and } P(B cap C)=frac{1}{4} `
`therefore P(frac{C}{B})=frac{P(B cap C)}{P(B)}=frac{frac{1}{4}}{frac{1}{3}}=frac{3}{4} { and } P(A^{prime} cap C^{prime})=1-P(A cup C)=1-[P(A)+P(C)-P(A cap C)] `

`=1-[frac{2}{5}+frac{1}{2}-frac{1}{5}]=1-[frac{4+5-2}{10}]=1-frac{7}{10}=frac{3}{10}`