Question

Two numbers are selected one by one without replacement at random from the set $S=\{1,2,3,4,5,6\}.$ The probability that the smaller 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

The correct option is D $\frac{4}{5}$

Total number of cases =${=}^6{P}_2=6\times 5=30$
Non-favorable cases are $(4,5),(5,4),(4,6),(6,4),(5,6),(6,5)$
Therefore probability that event will not happen $=\frac{6}{6\times 5}=\frac{1}{5}$
Hence required probability $=1-\frac{1}{5}=\frac{4}{5}$