Question

Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. what is the probability that you will draw two spades? express your first answer as a fraction in simplest form, and round your percent answer to the nearest hundredth.

Answer 1

The probability that you would draw two spades are 1/16

Explanation:

Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck.

The probability that you would draw both are spades.

We know that there are 13 spades in a deck of 52 cards. so the probability of first draw would be spade is

P1 =
`(13)/(52)= (1)/(4)`

From another deck you draw second card so the probability of second draw would be spade is

P2 =
`(13)/(52)= (1)/(4)`

Therefore, the probability of drawing two spades is

P =
`(1)/(4)` ×
`(1)/(4)` =
`(1)/(16)`

The probability that you would draw two spades are 1/16

Answer 2

There are 13 spades in one deck, so the probability to draw a spade from the first deck is

`P_1=(1)/(4)`

Similarly, the probability to draw a spade from the second deck is

`P_2=(1)/(4)`

The probability that both events occur (so, the probability we have to draw two spades from the two decks) is the product of the two probabilities, so:

`P=P_1 \cdot P_2 = (1)/(4) \cdot (1)/(4)= (1)/(16)`