Boxes B_1, B_2,and B_3 contain balls as given | vedclass

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

Question

(A) Let $W_i$ and $B_i$ denote the events of drawing a white ball and a black ball from box $B_i$ respectively. The probabilities are:For $B_1$: $P(W_

Vedclass · Accepted Answer

$\frac{5}{12}$

Vedclass · Answer

(A) Let $W_i$ and $B_i$ denote the events of drawing a white ball and a black ball from box $B_i$ respectively. The probabilities are:For $B_1$: $P(W_1) = \frac{1}{3}, P(B_1) = \frac{2}{3}$For $B_2$: $P(W_2) = \frac{3}{4}, P(B_2) = \frac{1}{4}$For $B_3$: $P(W_3) = \frac{2}{5}, P(B_3) = \frac{3}{5}$We want the probability of drawing two black balls and one white ball. This can happen in three mutually exclusive ways:$1$. $(W_1, B_2, B_3)$: $P(W_1) 	imes P(B_2) 	imes P(B_3) = \frac{1}{3} 	imes \frac{1}{4} 	imes \frac{3}{5} = \frac{3}{60}$$2$. $(B_1, W_2, B_3)$: $P(B_1) 	imes P(W_2) 	imes P(B_3) = \frac{2}{3} 	imes \frac{3}{4} 	imes \frac{3}{5} = \frac{18}{60}$$3$. $(B_1, B_2, W_3)$: $P(B_1) 	imes P(B_2) 	imes P(W_3) = \frac{2}{3} 	imes \frac{1}{4} 	imes \frac{2}{5} = \frac{4}{60}$The total probability is the sum of these probabilities:$P = \frac{3}{60} + \frac{18}{60} + \frac{4}{60} = \frac{25}{60} = \frac{5}{12}$

Boxes $B_1, B_2$,and $B_3$ contain balls as given below:
Box White Black
$B_1$ $1$ $2$
$B_2$ $3$ $1$
$B_3$ $2$ $3$

One ball is drawn at random from each box. Then,among the balls drawn,the probability that two are black and one is white,is

Similar Questions

$A$ die is formed so that the probability of getting a number $i$ when it is rolled is proportional to $i$ $(i=1, 2, 3, 4, 5, 6)$. The probability of getting an odd number on the die when it is rolled is

The probability that two randomly selected subsets of the set $\{1, 2, 3, 4, 5\}$ have exactly two elements in their intersection is:

If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$,then the value of $P(A' \cap B')$ is

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the events $A$ and $B$.

Statement-$I$: If a leap year is selected at random,the probability of it having $53$ Sundays is $2/7$.
Statement-$II$: $A$ leap year has $366$ days.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Boxes $B_1, B_2$,and $B_3$ contain balls as given below:BoxWhiteBlack$B_1$$1$$2$$B_2$$3$$1$$B_3$$2$$3$One ball is drawn at random from each box. Then,among the balls drawn,the probability that two are black and one is white,is