Question

A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). If two cards are drawn from the deck and then replaced back into the deck each time, what is the probability of drawing a heart and a spade from the deck of cards?

answer options:
1/8
1/26
1/16
1/32

Answer 1

`\large\boxed{(1)/(16)}`

The answer is equal to the probability of drawing a heart multiplied by the probability of drawing a spade.

The probability of a given suit being drawn is
`(13)/(54)`, which simplifies to
`(1)/(4)`. This is because there are 13 outcomes we would like out of 54 possible outcomes in total.

Multiply
`(1)/(4)` by itself (square it) to get the final answer of
`(1)/(16)`.

Answer corrected. Originally said
`(1)/(8)` as the final answer. Thank you, sangers1959!