A coin is tossed 7 times. What is the probabi | 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 obtained in $7$ tosses. Since the coin is fair,the probability of getting a head is $p = 1/2$ and the probability o

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(C) Let $X$ be the number of heads obtained in $7$ tosses. Since the coin is fair,the probability of getting a head is $p = 1/2$ and the probability of getting a tail is $q = 1/2$.The person wins if they get more heads than tails. Since there are $7$ tosses,the person wins if they get $4, 5, 6,$ or $7$ heads.The probability is given by the sum of binomial probabilities:$P(X \ge 4) = \sum_{k=4}^{7} \binom{7}{k} (1/2)^k (1/2)^{7-k} = \frac{1}{2^7} \sum_{k=4}^{7} \binom{7}{k}$We know that $\sum_{k=0}^{7} \binom{7}{k} = 2^7 = 128$.Also,by symmetry,$\sum_{k=0}^{3} \binom{7}{k} = \sum_{k=4}^{7} \binom{7}{k} = \frac{128}{2} = 64$.Therefore,the required probability is $\frac{64}{128} = \frac{1}{2}$.

$A$ coin is tossed $7$ times. What is the probability that a person who calls 'heads' every time wins more often?

Similar Questions

An unbiased die is tossed $500$ times. The standard deviation of getting sixes in these $500$ tosses is

In a binomial distribution $B(n, p = 1/4)$,if the probability of at least one success is $\geq 9/10$,then $n \geq$ ?

$A$ die is thrown $100$ times. The standard deviation of getting an even number 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

If the mean and the variance of a binomial variate $X$ are $1$ and $0.75$ respectively, then which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module