A pack of cards contains 4 aces,4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of these is an ace is A)9/12; B)3/16;C)1/6;D)1/9

Eliza Berry

Eliza Berry

Answered question

2023-03-13

A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of these is an ace is A920 B316 C16 D19

Answer & Explanation

Cooper Barker

Cooper Barker

Beginner2023-03-14Added 6 answers

The ideal decision is A 920
Justification for the ideal selection:
Step: 1 Find out the probability to get no ace.
There are 16 cards in all, including all aces, kings, queens, and jacks.
Cards to be drawn at random is 2.
Thus, number of ways to select 2 cards is C216.
Thus, the probability to get no ace is
=C212C216=12!×14!10!×16!=12×11×10!×14!10!×16×15×14!=1120
Step: 2 Find out the probability to get at least one ace.
Hence, the likelihood of getting at least one ace is
=1-1120=920
Therefore, Option(A) is the true answer.

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