A number is selected at random from the set { | vedclass

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

Question

(B) Let $S = \{1, 2, \ldots, 100\}$. The total number of elements is $100$.Let $A$ be the event that the number is divisible by $2$. The elements of $

Vedclass · Accepted Answer

$\frac{23}{50}$

Vedclass · Answer

(B) Let $S = \{1, 2, \ldots, 100\}$. The total number of elements is $100$.Let $A$ be the event that the number is divisible by $2$. The elements of $A$ are $\{2, 4, 6, \ldots, 100\}$. The number of elements in $A$ is $n(A) = 50$.Let $B$ be the event that the number is divisible by $3$ or $5$. We want to find the conditional probability $P(B|A) = \frac{n(A \cap B)}{n(A)}$.$A \cap B$ is the set of numbers in $\{1, 2, \ldots, 100\}$ that are divisible by $2$ $AND$ (divisible by $3$ $OR$ divisible by $5$).This is equivalent to numbers divisible by $6$ or $10$.Numbers divisible by $6$ up to $100$: $\lfloor \frac{100}{6} \rfloor = 16$.Numbers divisible by $10$ up to $100$: $\lfloor \frac{100}{10} \rfloor = 10$.Numbers divisible by both $6$ and $10$ (i.e.,divisible by $30$): $\lfloor \frac{100}{30} \rfloor = 3$.By the Principle of Inclusion-Exclusion, $n(A \cap B) = 16 + 10 - 3 = 23$.The required probability is $\frac{n(A \cap B)}{n(A)} = \frac{23}{50}$.

$A$ number is selected at random from the set $\{1, 2, \ldots, 100\}$. Given that the selected number is divisible by $2$, what is the probability that it is also divisible by $3$ or $5$?

Similar Questions

$A$ couple has two children. Find the probability that both children are females,if it is known that the elder child is a female.

If $A$ and $B$ are two events of a sample space $S$ such that $P(A)=0.2$,$P(B)=0.6$ and $P(A \mid B)=0.5$,then $P(A^{\prime} \mid B) = $

$A$ 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.

Two events $A$ and $B$ are given. If $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$,then what is the value of $P(B)$?

If $P(A | B) > P(A)$,then which of the following is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module