Question

A standard deck of 52 cards contains 13 cards each from the four suits: spades, clubs, diamonds and hearts. If two cards are randomly picked without replacement, what is the probability that they are both diamonds?

A. (13×13) / (52×52)
B. (13 / 52)
C. (13×12) / (52×51)
D. (13! / 52!)
E. (2 / 13)

Answer 1

(13/52)(12/51) = (13 × 12)/(52 × 51)

The correct answer is C.

Answer 2

The probability that two cards randomly picked from a standard 52-card deck are both diamonds is calculated by multiplying the probability of drawing a diamond on each draw without replacement, which gives (13/52) × (12/51). Thus, the correct answer is C. (13×12) / (52×51).

Step-by-step explanation:

To find the probability that two cards randomly picked from a standard 52-card deck are both diamonds, we follow these steps:

1. Calculate the probability of drawing the first diamond, which is 13 diamonds out of 52 cards total, so P(first diamond) = 13/52.
2. Since one card has been taken out and it was a diamond, there are now 12 diamonds left out of 51 cards. So, P(second diamond after first is diamond) = 12/51.
3. Multiply these two probabilities to get the overall probability of both events happening, which is (13/52) × (12/51).

The correct answer is C. (13×12) / (52×51).