When six coins are tossed simultaneously,the | vedclass

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

Question

(C) The total number of possible outcomes when tossing $6$ coins is $2^6 = 64$. We need to find the probability of getting at least $4$ heads,which is

Vedclass · Accepted Answer

$\frac{11}{32}$

Vedclass · Answer

(C) The total number of possible outcomes when tossing $6$ coins is $2^6 = 64$. We need to find the probability of getting at least $4$ heads,which is $P(X \ge 4) = P(X=4) + P(X=5) + P(X=6)$. Using the binomial distribution formula $P(X=r) = \binom{n}{r} p^r q^{n-r}$,where $n=6$ and $p=q=1/2$: $P(X=4) = \binom{6}{4} (1/2)^6 = \frac{15}{64}$ $P(X=5) = \binom{6}{5} (1/2)^6 = \frac{6}{64}$ $P(X=6) = \binom{6}{6} (1/2)^6 = \frac{1}{64}$ Summing these probabilities: $P(X \ge 4) = \frac{15+6+1}{64} = \frac{22}{64} = \frac{11}{32}$. Thus,the correct option is $C$.

When six coins are tossed simultaneously,the probability of getting at least $4$ heads is

Similar Questions

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:

The mean and variance of a binomial distribution are $4$ and $2$ respectively. Then the probability of exactly two successes is

The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. What is the probability that out of $5$ such bulbs,not more than one will fuse?

If $12$ identical balls are to be placed in $3$ distinct boxes,then the probability that one of the boxes contains exactly $3$ balls is:

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