Q14a. What is the probability that the card selected is either a queen or a black card?

Background

Topic: Probability with a Standard Deck of Cards

This question tests your understanding of the addition rule of probability, especially when events are not mutually exclusive (since a card can be both a queen and a black card).

Key Terms and Formulas

• Mutually Exclusive Events: Events that cannot happen at the same time.

• Addition Rule (Not Mutually Exclusive):

• = Probability of drawing a queen

• = Probability of drawing a black card

• = Probability of drawing a card that is both a queen and a black card

Step-by-Step Guidance

1. Determine the total number of cards in a standard deck (usually 52).

2. Count the number of queens in the deck and calculate .

3. Count the number of black cards in the deck and calculate .

4. Count the number of cards that are both queens and black (i.e., black queens) and calculate .

5. Set up the addition rule formula for not mutually exclusive events: .

6. Plug in the values you found for , , and , but do not compute the final probability yet.

Try solving on your own before revealing the answer!