Question

Two number are chosen at random from {1, 2, 3, 4, 5, 6, 7, 8} at a time. The probability that smaller of the two numbers is less than 4 is

• A. $\frac{7}{14}$
• B. $\frac{8}{14}$
• C. $\frac{9}{14}$
• D. $\frac{10}{14}$

Answer 1

Answer: (C)

$\frac{9}{14}$

${}^8{C}_2=$ all possible outcomes smallest of the 2 has is < 4.

If the smalls no, is 1 then $\{2,3,...8\}$ can be the others nos.

So, for 1, 7 outcomes

similarly, for 2, 6 outcomes

for 3, 5 outcomes

$P\left(A\right)=\frac{7+6+5}{8C_2}=\frac{9}{14}$