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?

(A) 0.0543
(B) 0.0588
(C) 0.0625
(D) 0.0643
(E) None of the above

Answer 1

(B) 0.0588

Explanation:

The probability is calculated as a division between the number of possibilities that satisfy a condition and the number of total possibilities. Then, the probability that the first card is diamonds is:

`P_1=(13)/(52)`

Because the deck has 52 cards and 13 of them are diamonds.

Then, if the first card was diamonds, the probability that the second card is also diamond is:

`P_2=(12)/(51)`

Because now, we just have 51 cards and 12 of them are diamonds.

Therefore, the probability that both cards are diamonds is calculated as a multiplication between
`P_1` and
`P_2`. This is:

`P=(13)/(52)*(12)/(51)=(1)/(17)=0.0588`