A box contains 24 identical balls,of which 12 | vedclass

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

Question

(C) The probability of drawing a white ball in a single draw is $p = \frac{12}{24} = \frac{1}{2}$.For the $4^{th}$ white ball to be drawn on the $7^{t

Vedclass · Accepted Answer

$\frac{5}{32}$

Vedclass · Answer

(C) The probability of drawing a white ball in a single draw is $p = \frac{12}{24} = \frac{1}{2}$.For the $4^{th}$ white ball to be drawn on the $7^{th}$ draw,there must be exactly $3$ white balls in the first $6$ draws,and the $7^{th}$ draw must be a white ball.This follows a binomial distribution scenario.The probability is given by: $P = \binom{6}{3} 	imes p^3 	imes (1-p)^3 	imes p$.Substituting $p = \frac{1}{2}$:$P = 20 	imes (\frac{1}{2})^3 	imes (\frac{1}{2})^3 	imes \frac{1}{2} = 20 	imes (\frac{1}{2})^7 = \frac{20}{128} = \frac{5}{32}$.

$A$ box contains $24$ identical balls,of which $12$ are white and $12$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is

Similar Questions

An experiment succeeds twice as often as it fails. Then the probability,that in the next $6$ trials there will be at least $4$ successes,is

Two cards are drawn successively with replacement from a fair deck of $52$ cards. Let $X$ denote the number of kings obtained when two cards are drawn. Then $E(X^2) = $

When two dice are rolled, let $x$ be the probability that the sum of the numbers appearing on the dice is at most $7$. Let $y$ be the probability of getting a sum of $7$ at least once when a pair of dice are rolled $n$ times. In order to have $y > x$, the minimum value of $n$ is

If $X \sim B(6, p)$ is a binomial variate and $\frac{P(X=4)}{P(X=2)}=\frac{1}{9}$, then $p=$

$8$ coins are tossed simultaneously. The probability of getting at least $6$ heads is

Vedclass Test Series

Exam Paper Generator

Online Exam Module