A pair of dice is thrown. Then the probabilit | vedclass

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

Question

(C) Let $E_1$ be the event that either of the dice shows $2$. Let $E_2$ be the event that the sum of the numbers on the dice is $6$. The sample space

Vedclass · Accepted Answer

$\frac{2}{5}$

Vedclass · Answer

(C) Let $E_1$ be the event that either of the dice shows $2$. Let $E_2$ be the event that the sum of the numbers on the dice is $6$. The sample space for the sum being $6$ is $E_2 = \{(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)\}$. Thus,the number of outcomes in $E_2$ is $n(E_2) = 5$. The outcomes where either of the dice shows $2$ given the sum is $6$ are $E_1 \cap E_2 = \{(2, 4), (4, 2)\}$. Thus,the number of outcomes in $E_1 \cap E_2$ is $n(E_1 \cap E_2) = 2$. The conditional probability is given by $P(E_1 | E_2) = \frac{n(E_1 \cap E_2)}{n(E_2)} = \frac{2}{5}$.

$A$ pair of dice is thrown. Then the probability that either of the dice shows $2$ when their sum is $6$ is

Similar Questions

Statement $- I :$ If $A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/5$,then $P(A|B) = 1/2$.
Statement $- II : P(A|B) = P(A)$ if $A$ and $B$ are independent events.

Let $A$ and $E$ be any two events with positive probabilities:
Statement $- 1$: $P(E/A) \geq P(A/E)P(E)$
Statement $- 2$: $P(A/E) \geq P(A \cap E)$

If $A$ and $B$ are two independent events,then $A$ and $\bar{B}$ are

It is given that $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$. Then $P(B) = $?

When a die is thrown twice,what is the probability that the sum of the numbers is $6$,given that at least one of the numbers is $4$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module