Question

Let E and F be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and probability that nine of them occurs in $\frac{2}{25}$. Then

• A. $P\left(E\right)=\frac{4}{5},P\left(F\right)=\frac{3}{5}$
• B. $P\left(E\right)=\frac{1}{5},P\left(F\right)=\frac{2}{5}$
• C. $P\left(E\right)=\frac{2}{5},P\left(F\right)=\frac{1}{5}$
• D. $P\left(E\right)=\frac{3}{5},P\left(F\right)=\frac{4}{5}$

Answer 1

Answer: (A), (D)

The correct options are
A $P\left(E\right)=\frac{4}{5},P\left(F\right)=\frac{3}{5}$
D $P\left(E\right)=\frac{3}{5},P\left(F\right)=\frac{4}{5}$

Let $P\left(E\right)=X,p\left(F\right)=y$
$X+y-2xy=\frac{11}{25},(1-x)(1-y)=\frac{2}{25}\Rightarrow xy=\frac{12}{25},x+y=\frac{7}{5}$
$\Rightarrow x=\frac{4}{5},y=\frac{3}{5}\left(or\right)x=\frac{3}{5},y=\frac{4}{5}$