At least how many times must a fair coin be t | vedclass

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

Question

(D) Let $n$ be the number of times the coin is tossed. Let $X$ be the number of heads obtained. $X$ follows a binomial distribution with parameters $n

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) Let $n$ be the number of times the coin is tossed. Let $X$ be the number of heads obtained. $X$ follows a binomial distribution with parameters $n$ and $p = \frac{1}{2}$.We are given that $P(X \ge 1) \ge 0.8$.Using the complement rule,$P(X \ge 1) = 1 - P(X = 0)$.So,$1 - P(X = 0) \ge 0.8 \Rightarrow P(X = 0) \le 0.2$.Since $P(X = 0) = \binom{n}{0} \left(\frac{1}{2}\right)^0 \left(1 - \frac{1}{2}\right)^n = \left(\frac{1}{2}\right)^n$,we have $\left(\frac{1}{2}\right)^n \le 0.2$.$\Rightarrow \frac{1}{2^n} \le \frac{1}{5} \Rightarrow 2^n \ge 5$.For $n = 1$,$2^1 = 2 For $n = 2$,$2^2 = 4 For $n = 3$,$2^3 = 8 \ge 5$.Thus,the minimum number of tosses required is $3$.

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

Similar Questions

For a binomial variate $X$ with $n=6$,if $P(X=2)=9 P(X=4)$,then its variance is

$A$ coin is tossed $n$ times. If the probability of getting $6$ heads is equal to the probability of getting $8$ heads,then find the value of $n$.

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

Find the probability of throwing at most $2$ sixes in $6$ throws of a single die.

Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. Let $X$ denote the random variable of the number of kings obtained in the two drawn cards. Then $P(X=1) + P(X=2)$ equals:

Vedclass Test Series

Exam Paper Generator

Online Exam Module