https://file.aiquickdraw.com/mathbot/file/1730053769326ljpez7nt.jpg

Let's analyze each part of the question.

### Part (a): Odds in favor of drawing a black jack
1. In a standard deck of 52 cards, there are 2 black jacks: the Jack of Spades and the Jack of Clubs.
2. The total number of possible outcomes is 52 (since there are 52 cards in the deck).
3. The number of favorable outcomes for drawing a black jack is 2.

The odds in favor of an event are calculated as:
\[
\text{Odds in favor} = \frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}
\]

So, the odds in favor of drawing a black jack are:
\[
\frac{2}{52 - 2} = \frac{2}{50} = \frac{1}{25}
\]

Thus, the odds in favor of drawing a black jack are \(1 : 25\).

---

### Part (b): Odds against drawing a face card
1. Face cards are Jacks, Queens, and Kings. There are 3 face cards in each suit (Hearts, Diamonds, Spades, and Clubs), totaling \(3 \times 4 = 12\) face cards in a deck.
2. The total number of possible outcomes is 52.
3. The number of unfavorable outcomes (non-face cards) is \(52 - 12 = 40\).

The odds against an event are calculated as:
\[
\text{Odds against} = \frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}
\]

So, the odds against drawing a face card are:
\[
\frac{40}{12} = \frac{10}{3}
\]

Thus, the odds against drawing a face card are \(10 : 3\).

---

Would you like further details on any of these calculations?

---

Here are five related questions that expand on this topic:

1. What are the odds of drawing a red card from a standard deck?
2. What are the odds against drawing a spade from a standard deck?
3. How would the odds change if we removed one face card from the deck?
4. What are the odds in favor of drawing a diamond that is not a face card?
5. If two cards are drawn consecutively without replacement, what are the odds in favor of drawing two black cards?

### Tip:
Remember that "odds" are different from "probability." While probability measures favorable outcomes over total outcomes, odds compare favorable outcomes to unfavorable outcomes.

Find the odds in favor of drawing a black jack and the odds against drawing a face card from a standard deck of 52 cards.

Explore how to find the odds in favor of drawing a black jack and the odds against drawing a face card in a standard deck of 52 cards. This problem covers key probability concepts suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation