Question

Four letters mailed today each have a probability of arriving in two days or sooner equal to $\frac{2}{3}$. Calculate the probability that exactly two of the four letters will arrive in two days or sooner.

• A. $\frac{4}{81}$
• B. $\frac{16}{81}$
• C. $\frac{6}{27}$
• D. $\frac{8}{27}$
• E. $\frac{4}{9}$

Answer 1

The correct option is D $\frac{8}{27}$

• probability of arriving in two days or sooner is $2/3$
• probability of arriving after two days is $1/3$.
• the probability that only two of four letters arrive in two days or sooner is ${{}^{4}C}_2\times 2/3\times 2/3\times 1/3\times 1/3=6\times 4/9\times 1/9=8/27$