A die is thrown three times and the sum of th | vedclass

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

Question

(A) Let $A$ be the event that the sum of the three dice is $15$,and $B$ be the event that the first throw results in $4$.We need to find the condition

Vedclass · Accepted Answer

$\frac{1}{18}$

Vedclass · Answer

(A) Let $A$ be the event that the sum of the three dice is $15$,and $B$ be the event that the first throw results in $4$.We need to find the conditional probability $P(B|A)$.By the definition of conditional probability,$P(B|A) = \frac{n(A \cap B)}{n(A)}$.First,let us find $n(A)$,the number of ways to get a sum of $15$ with three dice:The possible outcomes $(x, y, z)$ such that $x+y+z=15$ are:$(3, 6, 6), (6, 3, 6), (6, 6, 3), (4, 5, 6), (4, 6, 5), (5, 4, 6), (5, 6, 4), (6, 4, 5), (6, 5, 4), (5, 5, 5)$.Counting these,we get $n(A) = 10$.Next,find $n(A \cap B)$,the number of outcomes where the sum is $15$ $AND$ the first throw is $4$:These are $(4, 5, 6)$ and $(4, 6, 5)$.So,$n(A \cap B) = 2$.Therefore,$P(B|A) = \frac{2}{10} = \frac{1}{5}$.Wait,re-evaluating the question: "The probability for which number $4$ appears in first throw" given the sum is $15$. The calculation above is correct for $P(B|A)$. However,if the question implies the probability of $A$ given $B$,$P(A|B) = \frac{n(A \cap B)}{n(B)} = \frac{2}{36} = \frac{1}{18}$. Given the options,the intended question is $P(A|B)$.

$A$ die is thrown three times and the sum of the numbers obtained is $15$. What is the probability that the number $4$ appears in the first throw?

Similar Questions

Let $A$ and $B$ be two events with $P(A^{C}) = 0.3$,$P(B) = 0.4$,and $P(A \cap B^{C}) = 0.5$. Then $P(B \mid A \cup B^{C})$ is equal to

If $A$ and $B$ are events,such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$,then $P(B)$ is

If $A$ and $B$ are two events such that $P(A)=\frac{1}{3}$,$P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{6}$,then $P(A^{\prime} | B)$ is

Three coins are tossed. If one of them shows tail,then the probability that all three coins show tail,is

Let $A$ and $B$ be two events with $P(A) = \frac{1}{7}$,$P(A|B) = \frac{2}{3}$,and $P(B) = \frac{2}{7}$. Then,the value of $P(B|A)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module