Question

The probability of $A$ solving a riddle is $\frac{4}{5}$ and that of $B$ solving it is $\frac{2}{3}$. Find the probability that the problem will not be solved at all.

• A. $\frac{15}{91}$
• B. $\frac{4}{90}$
• C. $\frac{1}{15}$
• D. $\frac{1}{9}$

Answer 1

The correct option is C $\frac{1}{15}$

Given the probability that A solving the riddle is $P\left(A\right)=\frac{4}{5}$

and, the probability that B will solve the riddle is $P\left(B\right)=\frac{2}{3}$

Hence, the probability that the problem will not be solved $=$ none of them will solve is $\left(P\right(\overline{A})\times P(\overline{B}\left)\right)=\frac{1}{5}\times \frac{1}{3}$ $=\frac{1}{15}$