Two numbers are selected randomly from the set `S={1,2,3,4,5,6}` without replacement one by one. The probability that minimum of the two numbers is less than 4 is `1//15` b. `14//15` c. `1//5` d. `4//5`

Options

A. `(1)/(15)`
B. `(14)/(15)`
C. `(1)/(5)`
D. `(4)/(5)`

Answer

D

Explanation

The minimum of two numbers is less than 4 means at least one of them is less than 4.
Let `A_(i)` denote the event that the number selected in `i^(th)` draw is less than 4, where, i=1,2. Then,
Required probability `=P(A_(1) cup A_(2))=1-P(overline(A_(1)) cap overline(A_(2)))`
`=1-P(overline(A_(1)))P(overline(A_(2))//overline(A_(1)))=1-(3)/(6)xx(2)/(5)=(4)/(5)`