A single card is selected from an ordinary deck of cards. The sample space is shown in the figure below. Find the probabilities. (Enter the probabilities as fractions.)


(a) P(two of diamonds)
1

(b) P(two)
2

(c) P(diamond)
3

a) There is only one two of diamonds in the deck, therefore 1/52.

Use a similar process for the remaining two problems.

1/52

(a) P(two of diamonds) = 1/52

(b) P(two) = 4/52 = 1/13 (There are 4 twos in a deck of 52 cards: two of hearts, two of diamonds, two of clubs, two of spades)

(c) P(diamond) = 13/52 = 1/4 (There are 13 diamond cards in a deck of 52 cards)

To find the probabilities of the different events, we need to divide the number of favorable outcomes by the total number of possible outcomes.

(a) P(two of diamonds):
In a standard deck of 52 cards, there is only one two of diamonds. Therefore, the number of favorable outcomes is 1. The total number of possible outcomes is 52.

So, the probability of selecting the two of diamonds is 1/52.

(b) P(two):
In a standard deck of 52 cards, there are four twos (hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4. The total number of possible outcomes is 52.

So, the probability of selecting a two is 4/52, which simplifies to 1/13.

(c) P(diamond):
In a standard deck of 52 cards, there are 13 diamonds. Therefore, the number of favorable outcomes is 13. The total number of possible outcomes is 52.

So, the probability of selecting a diamond is 13/52, which simplifies to 1/4.