Two numbers are selected randomly from the se | vedclass

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

Question

(D) The total number of ways to select $2$ numbers from $6$ numbers without replacement where order matters is $P(6, 2) = 6 	imes 5 = 30$.Let $X$ and

Vedclass · Accepted Answer

$\frac{4}{5}$

Vedclass · Answer

(D) The total number of ways to select $2$ numbers from $6$ numbers without replacement where order matters is $P(6, 2) = 6 	imes 5 = 30$.Let $X$ and $Y$ be the two selected numbers. We want to find the probability that $\min(X, Y) It is easier to calculate the complement: the probability that $\min(X, Y) \ge 4$.If $\min(X, Y) \ge 4$,then both numbers must be chosen from the set $\{4, 5, 6\}$.The number of ways to choose $2$ numbers from $\{4, 5, 6\}$ without replacement is $P(3, 2) = 3 	imes 2 = 6$.The probability that $\min(X, Y) \ge 4$ is $\frac{6}{30} = \frac{1}{5}$.Therefore,the probability that $\min(X, Y) < 4$ is $1 - \frac{1}{5} = \frac{4}{5}$.

Two numbers are selected randomly from the set $S = \{ 1, 2, 3, 4, 5, 6 \}$ without replacement one by one. The probability that the minimum of the two numbers is less than $4$ is

Similar Questions

$A$ box contains $4$ red balls,$5$ green balls and $6$ white balls. $A$ ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?

In a single throw of $2$ dice,find the probability of getting a total of $11$.

$A$ five-digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetition. What is the probability that the number is divisible by $4$?

$A$ 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?

Two dice are thrown. If the first die shows $5$,then the probability that the sum of the numbers on both dice is $8$ or more than $8$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module