Question

Suppose that you draw two cards from a deck. After drawing the first card, you do not put the first card back in the deck. What is the probability (rounded to the nearest ten thousandth) that both cards are diamonds?

Answer 1

The correct answer is 0.05882.

Explanation:

A deck of cards have 52 cards, 13 cards of each suit.

We are drawing two cards without replacement.

We need to find the probability of getting a diamond as the first card.

Favorable outcomes are 13 and total number of outcomes are 52.

Thus this probability is
`(13)/(52) = (1)/(4)`.

Now for the next draw we again want to pick a diamond card.

Favorable outcomes are 12 and total number of leftover cards are 51.

Thus this probability is
`(12)/(51)`.

Now the probability that both cards are diamonds is
`(1)/(4)` ×
`(12)/(51)` =
`(3)/(51) = (1)/(17)` = 0.0588235 ≈ 0.05882