All the jacks, queens, kings, and aces of a regular 52 cards deck are taken out. The 16 cards are throughly shuffled and may opponent, a person who always tells the truth, simultaneously draws two cards at random and says, "I hold at least one ace". The probability that he holds two aces is

Options

A. `2//8`
B. `4//9`
C. `2//3`
D. `1//9`

Answer

D

Explanation

A: exactly oen ace
B: both aces
E: `AuuB`
`P(B//AuuB)=(""^(4)C_(2))/(""^(4)C_(1)""^(12)C_(1)+""^(4)C_(2))=6/54=1/9`