Question

A five-card hand is drawn from a standard 52-card deck all at once, so order doesn't matter. what is the probaility that the hand consists entirely of face crads (K, Q, and J are the ones called face cards)?

can i plese receive an explanation and help

Answer 1

33/108290 = 0.000305

Explanation:

There are 52 cards in a deck.

There are 3 face cards of each of 4 suits in a deck, so there are 12 face cards in a deck.

Taking all cards at once is the same as taking one card at a time with no replacement.

First card: p(face card) = 12/52 = 3/13

Now there are 11 face cards and a total of 51 cards left.

Second card: p(face card) = 11/51

Now there are 10 face cards and a total of 50 cards left.

Third card: p(face card) = 10/50 = 1/5

Now there are 9 face cards and a total of 49 cards left.

Fourth card: p(face card) = 9/49

Now there are 8 face cards and a total of 48 cards left.

Fifth card: p(face card) = 8/48 = 1/6

Since each drawing of a card is an independent event, the overall probability of drawing 5 face cards is the product of the individual probabilities.

p(5 face cards) = 3/13 × 11/51 × 1/5 × 9/49 × 1/6

p(5 face cards) = 33/108290 = 0.000305