lesson 1 homework - complements, unions, intersections
determine each probability.
1. randomly choosing the letter s from the letter in stars. 2. rolling a prime number on a die.
3. rolling a 5 on a die. 4. randomly choosing a blue marble from a bag of 5 blue marbles, 8 red marbles, and 7 yellow marbles.
5. a game spinner is green, red, and blue. the probability that the spinner will and on green is 15% and red is 35%. what is the probability the spinner will land on blue? 6. the probability of choosing a red marble from a bag is ⅓. what is the probability of not choosing a red marble?
7. you have a one in 50 chance of winning a raffle. what is the probability you will not win? 8. there is a one in 10 chance that you will be chosen as a class representative. what is the probability that you will not be chosen?
9. there is a 15% chance it will snow and a 15% it will rain. what is the probability that it will neither snow nor rain? 10. there is a 20% chance of a certain hurricane making landfall in south carolina. there is a 45% chance the hurricane will miss south carolina to the south. what is the probability the hurricane misses south carolina to the north?

Question

Accepted Answer

### Problem 1: Randomly choosing the letter S from the letters in STARS.
# Explanation:
## Step 1: Count total letters
The word "STARS" has 5 letters: S, T, A, R, S. So total number of letters $ n = 5 $.
## Step 2: Count number of S
Number of S in "STARS" is 2. Let $ m = 2 $.
## Step 3: Calculate probability
Probability $ P = \frac{m}{n} = \frac{2}{5} $.
# Answer: $\frac{2}{5}$

### Problem 2: Rolling a prime number on a die.
# Explanation:
## Step 1: Identify prime numbers on die
A die has numbers 1, 2, 3, 4, 5, 6. Prime numbers are 2, 3, 5. So number of prime numbers $ m = 3 $.
## Step 2: Total outcomes
Total outcomes when rolling a die $ n = 6 $.
## Step 3: Calculate probability
Probability $ P = \frac{m}{n} = \frac{3}{6} = \frac{1}{2} $.
# Answer: $\frac{1}{2}$

### Problem 3: Rolling a 5 on a die.
# Explanation:
## Step 1: Total outcomes
A die has 6 faces, so total outcomes $ n = 6 $.
## Step 2: Favorable outcomes
Only 1 face has 5, so favorable outcomes $ m = 1 $.
## Step 3: Calculate probability
Probability $ P = \frac{m}{n} = \frac{1}{6} $.
# Answer: $\frac{1}{6}$

### Problem 4: Randomly choosing a blue marble from a bag of 5 blue, 8 red, and 7 yellow marbles.
# Explanation:
## Step 1: Calculate total marbles
Total marbles $ n = 5 + 8 + 7 = 20 $.
## Step 2: Number of blue marbles
Number of blue marbles $ m = 5 $.
## Step 3: Calculate probability
Probability $ P = \frac{m}{n} = \frac{5}{20} = \frac{1}{4} $.
# Answer: $\frac{1}{4}$

### Problem 5: A game spinner is green, red, and blue. Probability of green is 15% and red is 35%. Probability of blue?
# Explanation:
## Step 1: Total probability
Total probability is 100% or 1. Let probability of blue be $ P(B) $.
## Step 2: Use probability sum
$ P(Green) + P(Red) + P(Blue) = 1 $. So $ 0.15 + 0.35 + P(B) = 1 $.
## Step 3: Solve for $ P(B) $
$ P(B) = 1 - 0.15 - 0.35 = 0.5 $ or 50%.
# Answer: $ 0.5 $ (or 50%)

### Problem 6: Probability of not choosing a red marble if probability of red is $ \frac{1}{3} $.
# Explanation:
## Step 1: Use complement rule
Probability of not choosing red $ P(\text{not red}) = 1 - P(\text{red}) $.
## Step 2: Substitute value
$ P(\text{not red}) = 1 - \frac{1}{3} = \frac{2}{3} $.
# Answer: $\frac{2}{3}$

### Problem 7: One in 50 chance of winning a raffle. Probability of not winning?
# Explanation:
## Step 1: Probability of winning
$ P(\text{win}) = \frac{1}{50} $.
## Step 2: Use complement rule
$ P(\text{not win}) = 1 - \frac{1}{50} = \frac{49}{50} $.
# Answer: $\frac{49}{50}$

### Problem 8: One in 10 chance of being chosen as class representative. Probability of not being chosen?
# Explanation:
## Step 1: Probability of being chosen
$ P(\text{chosen}) = \frac{1}{10} $.
## Step 2: Use complement rule
$ P(\text{not chosen}) = 1 - \frac{1}{10} = \frac{9}{10} $.
# Answer: $\frac{9}{10}$

### Problem 9: 15% chance of snow, 15% chance of rain. Probability of neither?
# Explanation:
## Step 1: Total probability of snow or rain
$ P(\text{snow or rain}) = 0.15 + 0.15 = 0.3 $.
## Step 2: Use complement rule
$ P(\text{neither}) = 1 - 0.3 = 0.7 $ or 70%.
# Answer: $ 0.7 $ (or 70%)

### Problem 10: 20% chance of hurricane making landfall in SC, 45% chance of missing to south. Probability of missing to north?
# Explanation:
## Step 1: Total probability
Total probability of all outcomes (landfall, miss south, miss north) is 1.
## Step 2: Set up equation
$ 0.2 + 0.45 + P(\text{miss north}) = 1 $.
## Step 3: Solve for $ P(\text{miss north}) $
$ P(\text{miss north}) = 1 - 0.2 - 0.45 = 0.35 $ or 35%.
# Answer: $ 0.35 $ (or 35%)

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QUESTION IMAGE

Question

Explanation:

Problem 1: Randomly choosing the letter S from the letters in STARS.

Step 1: Count total letters

Step 2: Count number of S

Step 3: Calculate probability

Step 1: Identify prime numbers on die

Step 2: Total outcomes

Step 3: Calculate probability

Step 1: Total outcomes

Step 2: Favorable outcomes

Step 3: Calculate probability

Answer:

Problem 2: Rolling a prime number on a die.