Questions: A card is drawn randomly from a standard 52-card deck. Find the probability of the given event. Write your answers as reduced fractions or whole numbers. (a) The card drawn is 5 P(5)= (b) The card drawn is the 5 of clubs. P(5 of clubs )=

Solution Steps

To solve these probability questions, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. For a standard 52-card deck, the total number of possible outcomes is 52.

(a) To find the probability of drawing a 5, we count the number of 5s in the deck. There are four 5s (one for each suit: hearts, diamonds, clubs, and spades).

(b) To find the probability of drawing the 5 of clubs, we consider that there is only one 5 of clubs in the deck.

In a standard deck of cards, the total number of cards is given by: \[ \text{Total outcomes} = 52 \]

The number of favorable outcomes for drawing a 5 (which includes the 5 of hearts, 5 of diamonds, 5 of clubs, and 5 of spades) is: \[ \text{Favorable outcomes for 5} = 4 \] Thus, the probability \( P(5) \) is calculated as: \[ P(5) = \frac{\text{Favorable outcomes for 5}}{\text{Total outcomes}} = \frac{4}{52} = \frac{1}{13} \]

The number of favorable outcomes for drawing the 5 of clubs is: \[ \text{Favorable outcomes for 5 of clubs} = 1 \] Therefore, the probability \( P(5 \text{ of clubs}) \) is: \[ P(5 \text{ of clubs}) = \frac{\text{Favorable outcomes for 5 of clubs}}{\text{Total outcomes}} = \frac{1}{52} \]

Final Answer