Question

A standard deck of cards has 52 cards in four suits: spades, hearts, diamonds, and clubs. Spades and clubs are black; hearts and diamonds are red. Each suit has 13 cards: 2 through 10, Jack, Queen, King, Ace. The "face cards" are the Jack, Queen, and King. Robby Billity shuffles a standard deck and draws one card. Then Robby replaces the card, shuffles again, and draws another card. He repeats this procedure for a total of 1000 draws. About how many times would we expect Robby to draw these cards?

Answer 1

231

Explanation:

Let's compute the probability of this event and then multiply it by 100.

As each deck has 4 suits and each suit has 3 faces, there are 12 faces in a deck.

As a deck has 52 cards, the probability of drawing a face is

12/52 = 0.23076

This means that if you choose a card 1000 times from a deck of poker cards, you probably will select 231 times a face (rounding to the nearest integer).