Question

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

• A. $\frac{1}{15}$
• B. $\frac{14}{15}$
• C. $\frac{1}{5}$
• D. $\frac{4}{5}$

Answer 1

Answer: (D)

$\frac{4}{5}$

Answer 2

The favourable cases are $12$ :

$(1, 2)$, $(1, 3)$, $(1, 4)$, $(1, 5)$, $(1, 6)$, $(2, 3)$, $(2, 4)$, $(2, 5)$,

$(2, 6)$, $(3, 4)$, $(3, 5)$, $(3, 6)$

The desired probability $= \frac{12}{^{6}C_{2}}=\frac{12}{15} = \frac{4}{5}$