Question

A pack of cards contains 4 aces, 4 kings,4 queens, 4 jacks. Two cards are drawn from the deck, find out the probability that at least one of them is ace.

Answer 1

To find the probability that at least one of the two cards drawn from the deck is an ace, we need to consider the different scenarios in which this can occur.
Let's calculate the probability using the principle of complementary probability, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
The total number of ways to choose 2 cards from a deck of 16 cards (4 aces, 4 kings, 4 queens, 4 jacks) is given by the combination formula: C(16, 2) = 16!/(2! * (16 - 2)!) = 120.
Now let's calculate the probability of drawing two non-ace cards:
The number of ways to choose 2 non-ace cards is given by C(12, 2) since there are 12 non-ace cards in the deck. C(12, 2) = 12! / (2! * (12 - 2)!) = 66. Therefore, the probability of drawing two non-ace cards is 66/120 = 11/20.
Now, the probability of drawing at least one ace can be calculated as the complement of drawing two non-ace cards:
Probability of drawing at least one ace = 1 - Probability of drawing two non-ace cards.
Probability of drawing at least one ace = 1 - (11/20) = 9/20.
So, the probability that at least one of the two cards drawn is an ace is 9/20.