The probability of getting either all heads o | vedclass

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

Question

(B) In each trial,three coins are tossed. The total number of outcomes is $2^3 = 8$.The outcomes for all heads $(HHH)$ or all tails $(TTT)$ are $2$.So

Vedclass · Accepted Answer

$\frac{3}{32}$

Vedclass · Answer

(B) In each trial,three coins are tossed. The total number of outcomes is $2^3 = 8$.The outcomes for all heads $(HHH)$ or all tails $(TTT)$ are $2$.So,the probability of getting all heads or all tails in one trial is $p = \frac{2}{8} = \frac{1}{4}$.The probability of not getting all heads or all tails is $q = 1 - p = 1 - \frac{1}{4} = \frac{3}{4}$.We want the event to occur for the second time in the $3^{rd}$ trial. This means in the first $2$ trials,the event must occur exactly once,and in the $3^{rd}$ trial,it must occur.The probability is given by: $P = (	ext{Probability of } 1 	ext{ success in } 2 	ext{ trials}) 	imes (	ext{Probability of success in } 3^{rd} 	ext{ trial})$.$P = \binom{2}{1} 	imes p^1 	imes q^1 	imes p = 2 	imes \frac{1}{4} 	imes \frac{3}{4} 	imes \frac{1}{4} = \frac{6}{64} = \frac{3}{32}$.

The probability of getting either all heads or all tails for exactly the second time in the $3^{rd}$ trial,if in each trial three coins are tossed,is

Similar Questions

Out of $100$ people selected at random,$10$ have a common cold. If five persons are selected at random from the group,then the probability that at most one person will have a common cold is

Five cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. What is the probability that none is a spade?

The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha}{3}$ respectively. If $P(X=1)=\frac{4}{243}$,then $P(X=4 \text{ or } 5)$ is equal to.

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 sum and product of the mean and variance of a binomial distribution are $82.5$ and $1350$ respectively. The number of trials in the binomial distribution is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module