Probability Questions of Cards

Problem Statement: A card is drawn at random from standard pack of cards. What is the probability that (i) it is either a king or queen, (ii) it is either a king or a black card?

(i) The probability of drawing a king card P(K) = 4/52

The probability of drawing a queen card P(Q) = 4/52

Since, both the events are mutually exclusive, the probability that the card drawn is either a king or queen is

P(K or Q) = P(K) + P(Q) = 4/52 + 4/52 = 8/52 = 4/26 = 2/13

(ii) The probability of drawing a king card P(K) = 4/52

The probability of drawing a black card P(B) = 26/52

Since, black kings are common to both, the events are not mutually exclusive.

Therefore, P(Black Kings) = 2/52

Thus, the probability that card drawn is either a king or a black card is

P(a king or black) = P(a king) + P(a black card) – P(a black king)

= 4/52 + 26/52 – 2/52 = 28/52

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Problem Statement: A card is drawn out of a pack of cards. Find the probability that the card is an ace, a king, a queen or a card of clubs.

Solution: The probability of drawing a card of ace, a king and a queen = P(A) = 12/52

The probability of drawing a card of club = P(B) = 13/52

Because the cards of ace, king and a queen can belong to club, therefore the events are not mutually exclusive.

The probability of drawing a card of an ace, a king and a queen of clubs = P(AB) = 3/52

So, the probability of drawing a card of an ace