One out of 9 ships is likely to sink when the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $p$ be the probability that a ship sinks,so $p = \frac{1}{9}$.Let $q$ be the probability that a ship arrives safely,so $q = 1 - \frac{1}{9} =

Vedclass · Accepted Answer

${}^6 C_3 \frac{8^3}{9^6}$

Vedclass · Answer

(B) Let $p$ be the probability that a ship sinks,so $p = \frac{1}{9}$.Let $q$ be the probability that a ship arrives safely,so $q = 1 - \frac{1}{9} = \frac{8}{9}$.We are looking for the probability that exactly $3$ ships sink out of $6$ ships.Using the binomial distribution formula $P(X=k) = {}^n C_k \cdot p^k \cdot q^{n-k}$,where $n=6$,$k=3$,$p=\frac{1}{9}$,and $q=\frac{8}{9}$:$P(X=3) = {}^6 C_3 \cdot \left(\frac{1}{9}\right)^3 \cdot \left(\frac{8}{9}\right)^3$$P(X=3) = {}^6 C_3 \cdot \frac{1}{9^3} \cdot \frac{8^3}{9^3}$$P(X=3) = {}^6 C_3 \cdot \frac{8^3}{9^6}$

One out of $9$ ships is likely to sink when they are set on sail. When $6$ ships are set on sail,the probability that exactly $3$ of them will not arrive safely is

Similar Questions

If $X \sim B(n, p)$, then the value of $\frac{P(X = k)}{P(X = k - 1)}$ is

The probability that a student is not a swimmer is $1/5$. What is the probability that $4$ out of $5$ students are swimmers?

$A$ fair coin is tossed a fixed number of times. If the probability of getting $5$ heads is equal to the probability of getting $4$ heads, then the probability of getting $6$ heads is

In a binomial distribution,the mean is $15$ and the variance is $10$. Then the parameter $n$ is:

If $X \sim B(35, p)$ such that $7 P(X=0)=P(X=1)$,then the value of $\frac{P(X=15)}{P(X=20)}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module