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(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

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