A box contains 4 black,2 white,and 6 red ball | vedclass

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

Question

(B) Let $E_1$ be the event that $1$ or $2$ appears on the die,and $E_2$ be the event that $3, 4, 5,$ or $6$ appears on the die.$P(E_1) = \frac{2}{6} =

Vedclass · Accepted Answer

$\frac{2}{13}$

Vedclass · Answer

(B) Let $E_1$ be the event that $1$ or $2$ appears on the die,and $E_2$ be the event that $3, 4, 5,$ or $6$ appears on the die.$P(E_1) = \frac{2}{6} = \frac{1}{3}$ and $P(E_2) = \frac{4}{6} = \frac{2}{3}$.Let $B$ be the event that a black ball is drawn.In the first box,there are $4$ black,$2$ white,and $6$ red balls (total $12$). So,$P(B|E_1) = \frac{4}{12} = \frac{1}{3}$.In the second box,there are $3$ black and $5$ white balls (total $8$). So,$P(B|E_2) = \frac{3}{8}$.By Bayes' theorem,the probability of $E_1$ given $B$ is $P(E_1|B) = \frac{P(E_1)P(B|E_1)}{P(E_1)P(B|E_1) + P(E_2)P(B|E_2)} = \frac{(1/3)(1/3)}{(1/3)(1/3) + (2/3)(3/8)} = \frac{1/9}{1/9 + 1/4} = \frac{1/9}{13/36} = \frac{4}{13}$.Since $E_1$ is the event that $1$ or $2$ appears,and the die is unbiased,$P(2|E_1) = \frac{1}{2}$.Thus,the probability that $2$ appeared given that the ball is black is $P(2|B) = P(2|E_1) 	imes P(E_1|B) = \frac{1}{2} 	imes \frac{4}{13} = \frac{2}{13}$.

Similar Questions

$A$ man is known to speak the truth $3$ out of $4$ times. He throws a die and reports that it is $6$. Then the probability that it is actually $6$ is:

Two bags $A$ and $B$ contain $2$ white,$3$ black,$4$ red balls and $3$ white,$4$ black,$5$ red balls respectively. $A$ ball is drawn from bag $A$ and transferred to bag $B$. If a ball is then drawn from bag $B$,what is the probability that the ball drawn from bag $B$ is white?

$A$ person is known to speak the truth $3$ out of $4$ times. If that person picks a card at random from a pack of $52$ cards and reports that it is a king,then the probability that it is actually a king is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Box	Red	White	Black
$A$	$1$	$6$	$3$
$B$	$6$	$2$	$2$
$C$	$8$	$1$	$1$
$D$	$0$	$6$	$4$