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 $F) =\frac{1}{4}+\frac{1}{2}-\frac{1}{8}=2+4-\frac{1}{8}=\frac{5}{8}$

(ii) From (i) , P(E orF) = P (E U F)$=\frac{5}{8}$

We have (EUF)=(E∩F) [By De Morgans 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)$=\frac{3}{8}$