A die is thrown 6 times. If 'getting an odd n | vedclass

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

Question

(A) The repeated tosses of a die are Bernoulli trials. Let $X$ denote the number of successes of getting odd numbers in an experiment of $n=6$ trials.

Vedclass · Accepted Answer

$\frac{3}{32}$

Vedclass · Answer

(A) The repeated tosses of a die are Bernoulli trials. Let $X$ denote the number of successes of getting odd numbers in an experiment of $n=6$ trials.The probability of getting an odd number in a single throw of a die is $p = \frac{3}{6} = \frac{1}{2}$.Therefore,the probability of failure is $q = 1 - p = 1 - \frac{1}{2} = \frac{1}{2}$.$X$ follows a binomial distribution with parameters $n=6$ and $p=\frac{1}{2}$.The probability mass function is given by $P(X=x) = ^{n}C_{x} p^{x} q^{n-x}$.We want to find the probability of $5$ successes,i.e.,$P(X=5)$.$P(X=5) = ^{6}C_{5} \left(\frac{1}{2}ight)^{5} \left(\frac{1}{2}ight)^{6-5}$.$P(X=5) = 6 	imes \left(\frac{1}{2}ight)^{5} 	imes \left(\frac{1}{2}ight)^{1} = 6 	imes \left(\frac{1}{2}ight)^{6}$.$P(X=5) = 6 	imes \frac{1}{64} = \frac{6}{64} = \frac{3}{32}$.

$A$ die is thrown $6$ times. If 'getting an odd number' is a success,what is the probability of $5$ successes?

Similar Questions

$A$ shooter can hit a given target with probability $\frac{1}{4}$. She keeps firing a bullet at the target until she hits it successfully three times and then she stops firing. The probability that she fires exactly six bullets lies in the interval

When a coin is tossed $6$ times,the probability of getting more heads than tails is

If $8$ coins are tossed simultaneously,what is the probability of getting at least $6$ heads?

If an unbiased die,marked with $-2, -1, 0, 1, 2, 3$ on its faces,is thrown five times,then the probability that the product of the outcomes is positive is:

$A$ fair coin is tossed $100$ times. The chance of getting a head an even number of times is

Vedclass Test Series

Exam Paper Generator

Online Exam Module