Question

If E and F are events such that P(E)=$\frac{1}{4}$ ,P(F)=$\frac{ 1}{2}$ and P(E and F)=$\frac{1}{8}$ ,find: (i) P(E or F),(ii) P(not E and not F).

Answer 1

Here, P(E) =$\frac{1}{4}$ , P(F) =$\frac{1}{2}$ , and P(E and F) =$\frac{1}{8}$
(i) We know that P(E or F) = P(E) + P(F) - P(E and F)
∴P(E or F) =$\frac{1}{4}+\frac{1}{2}-\frac{1}{8}=\frac{2+4-1}{8}=\frac{5}{8}$

(ii) From (i), P(E or F) = P (E U F) =$\frac{5}{8}$
We have (E'UF)'=(E∩F') [By De Morgan's law]
∴P(E'∩F')=P(EUF)'
Now,P(EUF)'=1-P(EUF)= $1-\frac{5}{8}=\frac{3}{8}$
∴P(E'∩F')= $\frac{3}{8}$
Thus,P(not E and not F)= $\frac{3}{8}$