https://file.aiquickdraw.com/mathbot/file/1728272781906as8kufrj.jpg

Let's solve the problem based on the image you provided.

### Part (a): Probability of drawing an Ace or Queen

- A standard deck of 52 cards has 4 aces and 4 queens, giving us a total of \(4 + 4 = 8\) cards that are either an ace or a queen.
- The probability \(P\) of drawing an ace or a queen is the ratio of favorable outcomes to total outcomes:

\[
P(\text{Ace or Queen}) = \frac{\text{Number of Aces or Queens}}{\text{Total Cards}} = \frac{8}{52} = \frac{2}{13}
\]

### Part (b): Odds in favor of drawing an Ace or Queen

- The odds in favor of an event are given by the ratio of favorable outcomes to unfavorable outcomes. There are 8 favorable outcomes (aces or queens) and \(52 - 8 = 44\) unfavorable outcomes (all other cards).
  
Thus, the odds in favor of drawing an ace or queen are:

\[
\text{Odds in favor} = \frac{\text{Favorable Outcomes}}{\text{Unfavorable Outcomes}} = \frac{8}{44} = \frac{2}{11}
\]

So, the odds in favor are \(2 : 11\).

### Final Answers:
- (a) The probability is \(\frac{2}{13}\).
- (b) The odds in favor are \(2 : 11\).

Would you like more details or have any questions?

Here are five related questions:
1. What is the probability of drawing a king or a jack from a standard deck?
2. How do the odds against drawing a face card compare to the odds in favor of it?
3. What are the odds of drawing a card that is a diamond?
4. How do you convert probability to odds?
5. How do the odds change if jokers are included in the deck?

**Tip:** To find the odds in favor of an event, remember it's the ratio of favorable to unfavorable outcomes, not the total number of outcomes like in probability.

For the experiment of drawing a single card from a standard 52-card deck, find (a) the probability of drawing an ace or a queen, and (b) the odds in favor of drawing an ace or a queen.

Learn how to calculate the probability and odds for drawing an ace or queen from a standard 52-card deck. This problem covers key concepts such as basic probability rules and odds calculations, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation