An unbiased coin is tossed n times. If the pr | vedclass

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

Question

(B) The probability of getting at least one head is given by $1 - P(	ext{no head})$.Since the coin is unbiased,the probability of getting no head in

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) The probability of getting at least one head is given by $1 - P(	ext{no head})$.Since the coin is unbiased,the probability of getting no head in $n$ tosses is $\left(\frac{1}{2}ight)^n$.Therefore,the probability of getting at least one head is $1 - \left(\frac{1}{2}ight)^n$.According to the problem,$1 - \left(\frac{1}{2}ight)^n > 0.8$.This simplifies to $1 - 0.8 > \left(\frac{1}{2}ight)^n$,which means $0.2 > \left(\frac{1}{2}ight)^n$.Writing $0.2$ as $\frac{1}{5}$,we get $\frac{1}{5} > \frac{1}{2^n}$,which implies $2^n > 5$.For $n=1$,$2^1 = 2 For $n=2$,$2^2 = 4 For $n=3$,$2^3 = 8 > 5$.Thus,the least value of $n$ is $3$.

An unbiased coin is tossed $n$ times. If the probability of getting at least one head is greater than $0.8$,then the least value of $n$ is

Similar Questions

If $X \sim B(n, p)$, then the value of $\frac{P(X = k)}{P(X = k - 1)}$ is

Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. Then the probability distribution of the number of kings is:

If $X$ has a binomial distribution with parameters $n=6, p$ and $P(X=2)=12, P(X=3)=5$,then $p=$

$A$ man takes a step forward with probability $0.4$ and one step backward with probability $0.6$. Then the probability that at the end of eleven steps he is one step away from the starting point is

In a shelf, there are $3$ mathematics and $2$ physics books. $A$ student takes a book randomly. If he takes a book randomly, successively for $3$ times by replacing the book already taken every time, then the mean of the number of mathematics books, which is treated as a random variable, is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module