Two numbers are selected at random from the s | vedclass

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

Question

(C) The set is $S = \{1, 2, 3, \ldots, 13\}$. There are $7$ odd numbers $\{1, 3, 5, 7, 9, 11, 13\}$ and $6$ even numbers $\{2, 4, 6, 8, 10, 12\}$.Let

Vedclass · Accepted Answer

$\frac{7}{12}$

Vedclass · Answer

(C) The set is $S = \{1, 2, 3, \ldots, 13\}$. There are $7$ odd numbers $\{1, 3, 5, 7, 9, 11, 13\}$ and $6$ even numbers $\{2, 4, 6, 8, 10, 12\}$.Let $E$ be the event that the sum of the two selected numbers is even. This happens if both numbers are odd or both numbers are even.Number of ways to select two odd numbers = $^7C_2 = \frac{7 	imes 6}{2} = 21$.Number of ways to select two even numbers = $^6C_2 = \frac{6 	imes 5}{2} = 15$.Total ways for the sum to be even = $21 + 15 = 36$.Let $A$ be the event that both numbers are odd. We want to find $P(A|E) = \frac{n(A \cap E)}{n(E)}$.Since $A \cap E$ is the event that both numbers are odd, $n(A \cap E) = 21$.Therefore, $P(A|E) = \frac{21}{36} = \frac{7}{12}$.

Two numbers are selected at random from the set $\{1, 2, 3, \ldots, 13\}$. If the sum of the selected numbers is even, what is the probability that both the numbers are odd?

Similar Questions

$A$ die is thrown twice and the sum of the numbers appearing is observed to be $6$. What is the conditional probability that the number $4$ has appeared at least once?

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

Given that $A$ and $B$ are two events such that $P(B) = \frac{3}{5}$,$P\left(\frac{A}{B}\right) = \frac{1}{2}$,and $P(A \cup B) = \frac{4}{5}$,then $P(A)$ is equal to:

$A$ die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of $4$. Then the conditional probability that the score $4$ has appeared at least once is

If $P(A / B) = \frac{3}{10}$, $P(B / A) = \frac{4}{5}$ and $P(A \cup B) = K P(B)$, then $\frac{1}{K} =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module