A die is thrown three times. Events A and B a | vedclass

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

Question

(A) The sample space $S$ for throwing a die three times has $6 	imes 6 	imes 6 = 216$ outcomes.Event $B$ is defined as $6$ on the first throw and $5

Vedclass · Accepted Answer

$\frac{1}{6}$

Vedclass · Answer

(A) The sample space $S$ for throwing a die three times has $6 	imes 6 	imes 6 = 216$ outcomes.Event $B$ is defined as $6$ on the first throw and $5$ on the second throw. Thus,$B = \{(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6)\}$.The number of outcomes in $B$ is $n(B) = 6$,so $P(B) = \frac{6}{216}$.Event $A$ is defined as $4$ on the third throw.The intersection $A \cap B$ consists of outcomes where $6$ is on the first,$5$ is on the second,and $4$ is on the third throw. Thus,$A \cap B = \{(6, 5, 4)\}$.The number of outcomes in $A \cap B$ is $n(A \cap B) = 1$,so $P(A \cap B) = \frac{1}{216}$.The conditional probability of $A$ given $B$ is $P(A|B) = \frac{P(A \cap B)}{P(B)}$.Substituting the values: $P(A|B) = \frac{1/216}{6/216} = \frac{1}{6}$.

$A$ die is thrown three times. Events $A$ and $B$ are defined as below:
$A$: $4$ on the third throw
$B$: $6$ on the first and $5$ on the second throw
Find the probability of $A$ given that $B$ has already occurred.

Similar Questions

If $A$ and $B$ are two independent events such that $P(A^{\prime}) = 0.75$,$P(A \cup B) = 0.65$ and $P(B) = p$,then the value of $p$ is

If $A$ and $B$ are two events such that $P(A) = 0.7$,$P(B) = 0.4$,and $P(A \cap \overline{B}) = 0.5$,where $\overline{B}$ denotes the complement of $B$,then $P(B \mid (A \cup \overline{B}))$ is equal to:

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) = $?

Two dice are thrown. If it is known that the sum of numbers on the dice was less than $6$,the probability of getting a sum as $3$ is:

In a hostel,$60 \%$ of the students read Hindi newspaper,$40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. $A$ student is selected at random. If she reads English newspaper,find the probability that she reads Hindi newspaper.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$A$ die is thrown three times. Events $A$ and $B$ are defined as below:$A$: $4$ on the third throw$B$: $6$ on the first and $5$ on the second throwFind the probability of $A$ given that $B$ has already occurred.