In a standard pack of cards there are 52 cards. The deck is made up of 4 suits of 13 cards each; red hearts, red diamonds, black clubs, and black spades. Each suit is made up of one of each of the following cards; ace, 2, 3, 4, 5, 6, 7, 8, 9, jack, queen, king; making 4 of each in the deck.(Ex: jack of heart, jack of diamonds, jack of clubs, and jack of spades). What is the probability of drawing a card that is a 9 or a diamond? Enter your answer as a reduced fraction (__/__).

To find the probability of drawing a card that is a 9 or a diamond, we need to first determine the number of favorable outcomes and the total number of possible outcomes.

In a standard deck of 52 cards, there are 4 cards that are 9s (one 9 of hearts, one 9 of diamonds, one 9 of clubs, and one 9 of spades) and 13 cards that are diamonds (one ace of diamonds, one 2 of diamonds, one 3 of diamonds, one 4 of diamonds, one 5 of diamonds, one 6 of diamonds, one 7 of diamonds, one 8 of diamonds, one 9 of diamonds, one 10 of diamonds, one jack of diamonds, one queen of diamonds, and one king of diamonds).

To find the number of favorable outcomes (i.e., cards that are either a 9 or a diamond), we add the number of 9 cards to the number of diamond cards, but we need to subtract the one 9 of diamonds from the total since it was already counted as a diamond.

Number of favorable outcomes = 4 (9 cards) + 13 (diamond cards) - 1 (9 of diamonds) = 16

The total number of possible outcomes is the total number of cards in the deck, which is 52.

Total number of possible outcomes = 52

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

= 16 / 52

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:

Probability = (16 ÷ 4) / (52 ÷ 4)

= 4 / 13

Therefore, the probability of drawing a card that is a 9 or a diamond is 4/13.