Introductory Statistics Practice Exam 2 Study Guide

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 for probability, especially when events are not mutually exclusive. You need to find the probability of selecting a card that is either a queen or a black card from a standard deck.

Key Terms and Formulas:

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

• Addition Rule for Probability (Not Mutually Exclusive):

$\text{P(A or B)} = \text{P(A)} + \text{P(B)} - \text{P(A and B)}$

• Standard deck: 52 cards (26 black, 26 red, 4 queens)

Step-by-Step Guidance

1. Identify the total number of cards in the deck: 52.

2. Count the number of queens in the deck: 4.

3. Count the number of black cards in the deck: 26 (spades and clubs).

4. Determine how many cards are both queens and black: 2 (queen of spades and queen of clubs).

5. Set up the addition rule formula: $\text{P(queen or black)} = \text{P(queen)} + \text{P(black)} - \text{P(queen and black)}$

6. Plug in the values for each probability, but do not calculate the final answer yet.

Try solving on your own before revealing the answer!

Final Answer: 0.423

$\text{P(queen)} = \frac{4}{52}$, $\text{P(black)} = \frac{26}{52}$, $\text{P(queen and black)} = \frac{2}{52}$

$\text{P(queen or black)} = \frac{4}{52} + \frac{26}{52} - \frac{2}{52} = \frac{28}{52} = 0.538$

Rounded to three decimal places: 0.538. This is the probability of selecting either a queen or a black card from a standard deck.