How many times must a man toss a fair coin so | vedclass

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

Question

(C) Let the man toss the coin $n$ times. The $n$ tosses are $n$ Bernoulli trials.Probability $(p)$ of getting a head at the toss of a coin is $\frac{1

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) Let the man toss the coin $n$ times. The $n$ tosses are $n$ Bernoulli trials.Probability $(p)$ of getting a head at the toss of a coin is $\frac{1}{2}$.$p = \frac{1}{2}, q = \frac{1}{2}$.Therefore,$P(X = x) = ^{n}C_{x} p^{x} q^{n-x} = ^{n}C_{x} (\frac{1}{2})^{x} (\frac{1}{2})^{n-x} = ^{n}C_{x} (\frac{1}{2})^{n}$.It is given that $P(	ext{getting at least one head}) > \frac{90}{100}$.$P(X \geq 1) > 0.9$.$1 - P(X = 0) > 0.9$.$1 - ^{n}C_{0} \cdot (\frac{1}{2})^{n} > 0.9$.$^{n}C_{0} \cdot (\frac{1}{2})^{n} $\frac{1}{2^{n}} $2^{n} > \frac{1}{0.1} = 10$.Since $2^{3} = 8$ and $2^{4} = 16$,the minimum value of $n$ that satisfies $2^{n} > 10$ is $4$.Thus,the man should toss the coin $4$ or more times.

How many times must a man toss a fair coin so that the probability of having at least one head is more than $90 \%$?

Similar Questions

$A$ variable $X$ takes values $0, 0, 2, 6, 12, 20, ..., n(n-1)$ with frequencies $^nC_0, ^nC_1, ^nC_2, ^nC_3, ^nC_4, ^nC_5, ..., ^nC_n$, respectively. If the mean of this data is $60$, then its median is:

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:

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

Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$,then $P(X \leq 3)=$

The probability that $A$ wakes up before the alarm rings is $0.4$. Then,the mean and variance of the number of times $A$ wakes up before the alarm rings,in the next $7$ days respectively are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module