A fair die is thrown 4 times. If getting a pr | vedclass

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

Question

(A) $1$. The sample space of a fair die is $S = \{1, 2, 3, 4, 5, 6\}$, so the total outcomes $n(S) = 6$.$2$. Prime numbers on a die are $\{2, 3, 5\}$,

Vedclass · Accepted Answer

$1/16$

Vedclass · Answer

(A) $1$. The sample space of a fair die is $S = \{1, 2, 3, 4, 5, 6\}$, so the total outcomes $n(S) = 6$.$2$. Prime numbers on a die are $\{2, 3, 5\}$, so the number of successful outcomes is $3$.$3$. Probability of success in a single throw, $p = 3/6 = 1/2$.$4$. Probability of failure in a single throw, $q = 1 - p = 1 - 1/2 = 1/2$.$5$. The die is thrown $n = 4$ times. The probability of getting no success (i.e., $0$ successes) is given by the binomial distribution formula $P(X = k) = \binom{n}{k} p^k q^{n-k}$.$6$. For $k = 0$, $P(X = 0) = \binom{4}{0} (1/2)^0 (1/2)^{4-0} = 1 	imes 1 	imes (1/2)^4 = 1/16$.

$A$ fair die is thrown $4$ times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is ...

Similar Questions

$A$ random variable $X$ follows a binomial distribution in which the difference between its mean and variance is $1$. If $2 P(X=2)=3 P(X=1)$,then $n^2 P(X>1)=$

If the mean and variance of a binomial distribution are $4$ and $2$ respectively,then the probability of getting $2$ successes is:

In a Binomial distribution $B(n, p)$,the sum and product of the mean and the variance are $5$ and $6$ respectively,then $6(n+p-q)=$

Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. Then the probability distribution of the number of jacks is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module