If a fair coin is tossed 8 times,then the pro | vedclass

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

Question

(C) Let $X$ be the number of heads in $8$ tosses of a fair coin. Here,$n=8$,$p=\frac{1}{2}$,and $q=\frac{1}{2}$.We want to find the probability that h

Vedclass · Accepted Answer

$\frac{93}{256}$

Vedclass · Answer

(C) Let $X$ be the number of heads in $8$ tosses of a fair coin. Here,$n=8$,$p=\frac{1}{2}$,and $q=\frac{1}{2}$.We want to find the probability that heads show more than tails,which means $X > 4$.Since the total number of outcomes is $2^8 = 256$,and the distribution is symmetric,we have $P(X  4)$.We know that $\sum_{k=0}^{8} P(X=k) = 1$,so $P(X  4) = 1$.Thus,$2P(X > 4) + P(X=4) = 1$,which implies $P(X > 4) = \frac{1 - P(X=4)}{2}$.Calculating $P(X=4) = {}^{8}C_{4} \left(\frac{1}{2}\right)^{8} = \frac{70}{256}$.Therefore,$P(X > 4) = \frac{1 - \frac{70}{256}}{2} = \frac{\frac{186}{256}}{2} = \frac{93}{256}$.

If a fair coin is tossed $8$ times,then the probability that it shows heads more than tails is

Similar Questions

$A$ lot of $100$ bulbs contains $10$ defective bulbs. Five bulbs are selected at random from the lot and sent to a retail store. The probability that the store will receive at most one defective bulb is:

How many times must a fair coin be tossed so that the probability of getting at least one head is at least $0.8$?

If the mean and variance of a binomial variable $X$ are $2$ and $1$ respectively,then what is the probability that $X \geq 1$?

One hundred identical coins,each with probability $p$ of showing up heads,are tossed once. If $0 < p < 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins,then the value of $p$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module