Question

Four cards are drawn at random from a pack of 52 well shuffled playing cards. find the probability of getting

one card of each suit

Answer 1

The probability of getting one card of each suit from a well-shuffled deck of 52 cards can be calculated using the concept of combinations. The probability is approximately 0.1058.

Step-by-step explanation:

The probability of getting one card of each suit can be found by using the concept of combinations.

1. There are 4 suits in a deck of cards: clubs, diamonds, hearts, and spades. Each suit has 13 cards.
2. To find the probability of getting one card of each suit, we need to calculate the number of combinations of 1 card from each suit out of the total 52 cards.
3. The total number of combinations of 4 cards from a set of 52 cards is given by the formula C(52, 4) = 52! / (4! * (52-4)!), where C(n, r) represents the number of combinations of r elements from a set of n elements.
4. Since we want 1 card from each suit, we need to multiply the number of combinations of 1 card from each suit: C(13, 1) * C(13, 1) * C(13, 1) * C(13, 1).
5. Finally, we divide this number by the total number of combinations of 4 cards to find the probability.

The probability of getting one card of each suit is given by:

(C(13, 1) * C(13, 1) * C(13, 1) * C(13, 1)) / C(52, 4) = (13 * 13 * 13 * 13) / (270725) = 0.1058.