A bag contains 6 white and 4 black balls. A d | vedclass

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

Question

(C) Let $X$ be the number obtained on the die. $X \in \{1, 2, 3, 4, 5, 6\}$,each with probability $\frac{1}{6}$.If $X=k$,the number of ways to draw $k

Vedclass · Accepted Answer

$\frac{1}{5}$

Vedclass · Answer

(C) Let $X$ be the number obtained on the die. $X \in \{1, 2, 3, 4, 5, 6\}$,each with probability $\frac{1}{6}$.If $X=k$,the number of ways to draw $k$ white balls from $6$ white balls is $\binom{6}{k}$,and the total number of ways to draw $k$ balls from $10$ balls is $\binom{10}{k}$.The probability of drawing $k$ white balls given $X=k$ is $P(W|X=k) = \frac{\binom{6}{k}}{\binom{10}{k}}$.The total probability is $P(W) = \sum_{k=1}^{6} P(X=k) 	imes P(W|X=k) = \frac{1}{6} \sum_{k=1}^{6} \frac{\binom{6}{k}}{\binom{10}{k}}$.Calculating the terms:$k=1: \frac{6}{10} = \frac{3}{5} = 0.6$$k=2: \frac{15}{45} = \frac{1}{3} \approx 0.333$$k=3: \frac{20}{120} = \frac{1}{6} \approx 0.167$$k=4: \frac{15}{210} = \frac{1}{14} \approx 0.071$$k=5: \frac{6}{252} = \frac{1}{42} \approx 0.024$$k=6: \frac{1}{210} \approx 0.005$Summing these: $\frac{1}{6} \left( \frac{6}{10} + \frac{15}{45} + \frac{20}{120} + \frac{15}{210} + \frac{6}{252} + \frac{1}{210} ight) = \frac{1}{6} \left( \frac{3}{5} + \frac{1}{3} + \frac{1}{6} + \frac{1}{14} + \frac{1}{42} + \frac{1}{210} ight) = \frac{1}{6} \left( \frac{126+70+35+15+5+1}{210} ight) = \frac{1}{6} 	imes \frac{252}{210} = \frac{42}{210} = \frac{1}{5}$.

$A$ bag contains $6$ white and $4$ black balls. $A$ die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:

Similar Questions

$A$ box contains $10$ red marbles,$20$ blue marbles,and $30$ green marbles. If $5$ marbles are drawn from the box,what is the probability that at least one will be green?

Two persons each make a single throw with a die. The probability they get equal value is $p_1$. Four persons each make a single throw and the probability of exactly three being equal is $p_2$,then:

$A$ committee consists of $9$ experts taken from three institutions $A, B$,and $C$,of which $2$ are from $A$,$3$ from $B$,and $4$ from $C$. If three experts resign,then the probability that they belong to different institutions is

In a consignment of $15$ articles,it is found that $3$ are defective. If a sample of $5$ articles is chosen at random from it,then the probability of having $2$ defective articles is

If $6$ girls and $5$ boys are sitting in a row,what is the probability that no two boys sit together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module