Two coins are tossed 5 times. What is the pro | vedclass

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

Question

(D) When two coins are tossed,the number of heads in one trial can be $0, 1,$ or $2$. In $5$ trials,the total number of tosses is $10$. Let $X$ be the

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(D) When two coins are tossed,the number of heads in one trial can be $0, 1,$ or $2$. In $5$ trials,the total number of tosses is $10$. Let $X$ be the total number of heads in $10$ independent tosses of a single coin. $X$ follows a binomial distribution $B(n, p)$ with $n = 10$ and $p = 1/2$. We want the probability that $X$ is odd,i.e.,$P(X \in \{1, 3, 5, 7, 9\})$. $P(X 	ext{ is odd}) = \sum_{k \in \{1, 3, 5, 7, 9\}} \binom{10}{k} (\frac{1}{2})^k (\frac{1}{2})^{10-k} = (\frac{1}{2})^{10} \sum_{k \in \{1, 3, 5, 7, 9\}} \binom{10}{k}$. Using the property of binomial coefficients,$\sum_{k 	ext{ odd}} \binom{n}{k} = 2^{n-1}$. Here,$n = 10$,so the sum is $2^{10-1} = 2^9$. Therefore,$P(X 	ext{ is odd}) = \frac{2^9}{2^{10}} = \frac{1}{2}$.

Two coins are tossed $5$ times. What is the probability of getting an odd number of heads?

Similar Questions

The probability that a certain kind of component will survive a given test is $\frac{2}{3}$. The probability that at most $2$ components out of $4$ tested will survive is

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

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

In a random experiment of throwing $5$ coins, the number of heads is defined as a random variable. The mean of the random variable is

For a binomial variate $X$, if $n=4$ and $P(X=4)=6 P(X=2)$, then the value of $p$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module