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(B) The total number of ways to select $2$ digits from $8$ digits without replacement is $^8C_2 = \frac{8 	imes 7}{2} = 28$.Let $X$ be the minimum of

Vedclass · Accepted Answer

$\frac{11}{14}$

Vedclass · Answer

(B) The total number of ways to select $2$ digits from $8$ digits without replacement is $^8C_2 = \frac{8 	imes 7}{2} = 28$.Let $X$ be the minimum of the two selected digits. We want to find $P(X It is easier to calculate the complement: $P(X $X \geq 5$ means both selected digits must be from the set $\{5, 6, 7, 8\}$.The number of ways to choose $2$ digits from these $4$ digits is $^4C_2 = \frac{4 	imes 3}{2} = 6$.Therefore,$P(X \geq 5) = \frac{6}{28} = \frac{3}{14}$.Thus,$P(X < 5) = 1 - \frac{3}{14} = \frac{11}{14}$.

Two digits are selected randomly from the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$ without replacement one by one. The probability that the minimum of the two digits is less than $5$ is

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