Two dice are thrown simultaneously. If A is t | vedclass

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

Question

(B) When two dice are thrown,the total number of outcomes is $n(S) = 6 	imes 6 = 36$. Event $A$ is the event of getting a sum $\ge 8$. The outcomes a

Vedclass · Accepted Answer

$\frac{6}{15}$

Vedclass · Answer

(B) When two dice are thrown,the total number of outcomes is $n(S) = 6 	imes 6 = 36$. Event $A$ is the event of getting a sum $\ge 8$. The outcomes are: $A = \{(2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5), (6,6)\}$. Thus,$n(A) = 15$. Event $B$ is the event of getting a number $\le 3$ on at least one die. Event $A \cap B$ is the event of getting a sum $\ge 8$ $AND$ at least one die showing a number $\le 3$. Looking at the elements of $A$,the outcomes where at least one die is $\le 3$ are: $A \cap B = \{(2,6), (3,5), (3,6), (5,3), (6,2), (6,3)\}$. Thus,$n(A \cap B) = 6$. The conditional probability is given by $P(B / A) = \frac{n(A \cap B)}{n(A)} = \frac{6}{15} = \frac{2}{5}$.

Two dice are thrown simultaneously. If $A$ is the event of getting the sum of the numbers on two dice as greater than or equal to $8$ and $B$ is the event of getting a number less than or equal to $3$ on at least one of the dice. Then,$P(B / A) = $

Similar Questions

Two dice are rolled. If $A$ denotes the event that the same number shows on each die and $B$ denotes the event that the sum of the numbers on both dice is greater than $7$,then $P(A \mid B)$ and $P(B \mid A)$ respectively are

If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$,then $P(B/A) = $

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

If $A$ and $B$ are two independent events,then $P\left( \frac{A}{B} \right) = $

$A$ black and a red dice are rolled. Find the conditional probability of obtaining the sum $8$,given that the red die resulted in a number less than $4$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module