determine the probability of each situation.
1. a bag contains 25 marbles: 10 black, 13 red, and 2 blue. what is the probability of getting a red or a blue marble?
2. what is the probability of drawing a jack or a club from a standard deck of playing cards?
3. numbers 1 - 10 are written on cards and placed in a bag. what is the probability of choosing 8 or choosing a number less than 5?
4. the letters a - p are written on cards and placed in a bag. what is the probability of choosing an e or choosing a vowel?
5. a spinner contains the numbers 3, 4, 5, and 6 on equal sized wedges. what is the probability of spinning an even number or a number greater than 5?
6. what is the probability of rolling an even number or an odd number on a standard 6 -sided die?
7. what is the probability of drawing an ace or a queen from a standard deck of playing cards?
8. what is the probability of drawing a king or a red card from a standard deck of playing cards?

Question

Accepted Answer

### Problem 1
# Explanation:
## Step1: Identify favorable and total outcomes
Total marbles = 25. Red marbles = 13, Blue marbles = 2.
## Step2: Calculate probabilities and sum
Probability of red: $P(	ext{red}) = \frac{13}{25}$, Probability of blue: $P(	ext{blue}) = \frac{2}{25}$. Since mutually exclusive, $P(	ext{red or blue}) = \frac{13}{25} + \frac{2}{25} = \frac{15}{25} = \frac{3}{5}$.
# Answer: $\frac{3}{5}$

### Problem 2
# Explanation:
## Step1: Recall deck composition
Standard deck: 52 cards. Jacks: 4, Clubs: 13, Jack of Clubs: 1 (overlap).
## Step2: Apply inclusion - exclusion principle
$P(	ext{Jack or Club}) = P(	ext{Jack}) + P(	ext{Club}) - P(	ext{Jack and Club}) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$.
# Answer: $\frac{4}{13}$

### Problem 3
# Explanation:
## Step1: Identify favorable outcomes
Numbers 1 - 10. Number 8: 1 outcome. Numbers less than 5: 1,2,3,4 (4 outcomes). No overlap.
## Step2: Calculate probability
Total outcomes = 10. $P(8 	ext{ or } <5) = \frac{1 + 4}{10} = \frac{5}{10} = \frac{1}{2}$.
# Answer: $\frac{1}{2}$

### Problem 4
# Explanation:
## Step1: Identify favorable outcomes
Letters A - P (16 letters). Vowels in A - P: A, E, I, O, U? Wait, A - P: vowels are A, E, I, O? Wait, A - P: letters are A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P. Vowels: A, E, I, O (4 vowels). E is a vowel, so overlap (E is counted in both).
## Step2: Apply inclusion - exclusion
$P(E 	ext{ or vowel}) = P(E) + P(	ext{vowel}) - P(E 	ext{ and vowel}) = \frac{1}{16} + \frac{4}{16} - \frac{1}{16} = \frac{4}{16} = \frac{1}{4}$. Wait, correction: vowels in A - P: A, E, I, O (4). So E is one of the vowels. So number of favorable: vowels (4) since E is already a vowel. Wait, no: choosing E or a vowel. The set of E or vowel is just the set of vowels (since E is a vowel). Wait, no: if we consider "E or vowel", it's the union. But E is a vowel, so the union is the set of vowels. Wait, maybe I made a mistake. Let's list: vowels in A - P: A, E, I, O (4 letters). E is one of them. So the number of outcomes for "E or vowel" is 4 (since E is already in vowels). Total outcomes: 16. So $P = \frac{4}{16} = \frac{1}{4}$. Wait, but let's do it properly. $P(E) = \frac{1}{16}$, $P(	ext{vowel}) = \frac{4}{16}$, $P(E \cap 	ext{vowel}) = \frac{1}{16}$ (since E is a vowel). So $P(E \cup 	ext{vowel}) = \frac{1}{16}+\frac{4}{16}-\frac{1}{16}=\frac{4}{16}=\frac{1}{4}$.
# Answer: $\frac{1}{4}$

### Problem 5
# Explanation:
## Step1: Identify favorable outcomes
Spinner numbers: 3,4,5,6. Even numbers: 4,6 (2 outcomes). Numbers >5: 6 (1 outcome). Overlap: 6.
## Step2: Apply inclusion - exclusion
$P(	ext{even or }>5) = P(	ext{even}) + P(>5) - P(	ext{even and }>5) = \frac{2}{4} + \frac{1}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$.
# Answer: $\frac{1}{2}$

### Problem 6
# Explanation:
## Step1: Identify outcomes
Die: 1 - 6. Even numbers: 2,4,6 (3), Odd numbers: 1,3,5 (3). Mutually exclusive and exhaustive.
## Step2: Calculate probability
$P(	ext{even or odd}) = \frac{3 + 3}{6} = \frac{6}{6} = 1$.
# Answer: $1$

### Problem 7
# Explanation:
## Step1: Identify outcomes
Deck: 52 cards. Aces: 4, Queens: 4. Mutually exclusive (no card is both Ace and Queen).
## Step2: Calculate probability
$P(	ext{Ace or Queen}) = \frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \frac{2}{13}$.
# Answer: $\frac{2}{13}$

### Problem 8
# Explanation:
## Step1: Identify outcomes
Deck: 52 cards. Kings: 4, Red cards: 26, Red Kings: 2 (overlap).
## Step2: Apply inclusion - exclusion
$P(	ext{King or red}) = P(	ext{King}) + P(	ext{red}) - P(	ext{King and red}) = \frac{4}{52} + \frac{26}{52} - \frac{2}{52} = \frac{28}{52} = \frac{7}{13}$.
# Answer: $\frac{7}{13}$

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QUESTION IMAGE

Question

Explanation:

Problem 1

Step1: Identify favorable and total outcomes

Step2: Calculate probabilities and sum

Step1: Recall deck composition

Step2: Apply inclusion - exclusion principle

Step1: Identify favorable outcomes

Step2: Calculate probability

Answer:

Problem 2