Question

The probability that a ship safely reaches a port is $\frac{1}{3}$. The probability that out of $5$ ships, at least $4$ ships would arrive safely is

• A. $\frac{1}{243}$
• B. $\frac{10}{243}$
• C. $\frac{11}{243}$
• D. $\frac{13}{243}$

Answer 1

The correct option is C $\frac{11}{243}$

This is a case of binomial distribution with $p=\frac{1}{3}$, $n=5$ and $r=4$.

Also, $P(X=r){=}^n{C}_r{p}^r(1-p{)}^{n-r}$

We need to find $P(X\ge 4)=P(X=4)+P(X+5){=}^5{C}_4{\left(\frac{1}{3}\right)}^4\left(\frac{2}{3}\right){+}^5{C}_5{\left(\frac{1}{3}\right)}^5{\left(\frac{2}{3}\right)}^0=\frac{11}{243}$