For a biased die,the probabilities for differ | vedclass

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

Question

(A) Let $E_1$ be the event that face $1$ turns up and $E_2$ be the event that face $2$ turns up.Given probabilities are $P(E_1) = 0.1$ and $P(E_2) = 0

Vedclass · Accepted Answer

$\frac{5}{21}$

Vedclass · Answer

(A) Let $E_1$ be the event that face $1$ turns up and $E_2$ be the event that face $2$ turns up.Given probabilities are $P(E_1) = 0.1$ and $P(E_2) = 0.32$.We are given that either face $1$ or $2$ has turned up. Let this event be $A = E_1 \cup E_2$.Since $E_1$ and $E_2$ are mutually exclusive,$P(A) = P(E_1) + P(E_2) = 0.1 + 0.32 = 0.42$.We need to find the conditional probability $P(E_1 | A)$,which is the probability that face $1$ has turned up given that either $1$ or $2$ has turned up.$P(E_1 | A) = \frac{P(E_1 \cap A)}{P(A)} = \frac{P(E_1)}{P(A)} = \frac{0.1}{0.42}$.Simplifying the fraction: $\frac{0.1}{0.42} = \frac{10}{42} = \frac{5}{21}$.

$Face$	$1$	$2$	$3$	$4$	$5$	$6$
$Probability$	$0.1$	$0.32$	$0.21$	$0.15$	$0.05$	$0.17$

For a biased die,the probabilities for different faces to turn up are given below:

$Face$ $1$ $2$ $3$ $4$ $5$ $6$

$Probability$ $0.1$ $0.32$ $0.21$ $0.15$ $0.05$ $0.17$

The die is tossed and you are told that either face $1$ or $2$ has turned up. Then the probability that it is face $1$ is:

Similar Questions

When $2$ dice are thrown, it is observed that the sum of the numbers appearing on the top faces of both dice is a prime number. What is the probability that at least one of the numbers in the pair is a multiple of $3$?

If $P(A) = \frac{6}{11}$,$P(B) = \frac{5}{11}$ and $P(A \cup B) = \frac{7}{11}$,find $P(A | B)$.

If $A$ and $B$ are two events such that $P(A)=\frac{1}{2}$,$P(B)=\frac{1}{2}$ and $P(A \mid B)=\frac{1}{4}$,then $P(A^{\prime} \cap B^{\prime})$ is

If $4\,P(A) = 6\,P(B) = 10\,P(A \cap B) = 1$,then $P\left( \frac{B}{A} \right) = \dots$

If $2$ cards drawn at random from a well-shuffled pack of $52$ playing cards are from the same suit, then the probability of getting a face card and a card having a prime number is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

For a biased die,the probabilities for different faces to turn up are given below: $Face$ $1$ $2$ $3$ $4$ $5$ $6$ $Probability$ $0.1$ $0.32$ $0.21$ $0.15$ $0.05$ $0.17$ The die is tossed and you are told that either face $1$ or $2$ has turned up. Then the probability that it is face $1$ is: