Questions: Suppose you draw a card from a well-shuffled deck of 52 cards. What is the probability of drawing a 5 or a jack? P(5 or jack )= (Simplify your answer. Type an integer or a fraction.)

$Suppose you draw a card from a well-shuffled deck of 52 cards. What is the probability of drawing a 5 or a jack? P(5 or jack )= (Simplify your answer. Type an integer or a fraction.)$

Transcript text: Suppose you draw a card from a well-shuffled deck of 52 cards. What is the probability of drawing a 5 or a jack? \[ P(5 \text { or jack })= \] $\square$ (Simplify your answer. Type an integer or a fraction.)

Solution

Solution Steps

To find the probability of drawing a 5 or a jack from a standard deck of 52 cards, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. There are 4 fives and 4 jacks in the deck, making a total of 8 favorable outcomes. The probability is then the number of favorable outcomes divided by the total number of cards in the deck.

Step 1: Total Outcomes

The total number of cards in a standard deck is given by: \[ \text{Total cards} = 52 \]

Step 2: Favorable Outcomes

The number of favorable outcomes for drawing a 5 or a jack is calculated as follows: \[ \text{Number of 5s} = 4 \] \[ \text{Number of jacks} = 4 \] Thus, the total number of favorable outcomes is: \[ \text{Favorable outcomes} = 4 + 4 = 8 \]

Step 3: Probability Calculation

The probability $ P $ of drawing a 5 or a jack is given by the ratio of favorable outcomes to total outcomes: \[ P(5 \text{ or jack}) = \frac{\text{Favorable outcomes}}{\text{Total cards}} = \frac{8}{52} \] This simplifies to: \[ P(5 \text{ or jack}) = \frac{2}{13} \approx 0.1538 \]