Question

1. the spinner shown is spun once. what is the sample space? (example 1)2. each letter in the word mississippi is written on a piece of paper and placed into a bag. a letter is drawn at random. what is the sample space? (example 1)3. a teacher placed the letter cards e, l, o, r, u, and w in a bag. a card is drawn at random. determine the theoretical probability for drawing a card that has a vowel on it. (example 2)4. a player in a board game rolls a six-sided number cube labeled 1 through 6 once. determine the theoretical probability of rolling a 1 or 2. (example 2)5. the table shows the lengths of time for rides at a fair. zane will choose a ride at random and wants to find the probability of choosing a ride that lasts less than 200 seconds. what is the probability of the complement of the event? describe the complement. (example 3)|ride|time (seconds)|| ---- | ---- ||barrel|150||bumper cars|195||circus carousel|210||log ride|120||roller coaster|55||swings|225||train|300||zero gravity spinner|65|6. red is spun on a spinner with five equal-size sections labeled red, yellow, blue, green, and purple. what is the probability of the complement of the event? describe the complement. (example 3)test practice7. multiselect a sportscaster predicted that the local high school baseball team has a 75% chance of winning tonight. select all of the values that represent the probability of the team not winning.□ 0.75□ 25%□ 0.25□ $\frac{3}{4}$□ 75%□ $\frac{1}{4}$

Explanation:

Step1: List spinner outcomes

$\{2, 3, 4, 5\}$

Step2: List unique MISSISSIPPI letters

$\{\text{M}, \text{I}, \text{S}, \text{P}\}$

Step3: Count vowels and total cards

Vowels: E, O, U (3 total). Total cards: 6.
Probability: $\frac{3}{6} = \frac{1}{2}$

Step4: Count favorable roll outcomes

Favorable: 1, 2 (2 total). Total outcomes: 6.
Probability: $\frac{2}{6} = \frac{1}{3}$

Step5: Identify complement event

Complement: Rides ≥200 seconds. Count these: Circus Carousel, Swings, Train (3 total). Total rides: 8.
Probability: $\frac{3}{8}$

Step6: Identify complement event

Complement: Spinning yellow, blue, green, purple (4 outcomes). Total sections: 5.
Probability: $\frac{4}{5}$

Step7: Calculate non-winning probability

$1 - 0.75 = 0.25 = 25\% = \frac{1}{4}$

Answer:

1. $\{2, 3, 4, 5\}$
2. $\{\text{M}, \text{I}, \text{S}, \text{P}\}$
3. $\frac{1}{2}$
4. $\frac{1}{3}$
5. $\frac{3}{8}$; The complement is choosing a ride that lasts 200 seconds or longer.
6. $\frac{4}{5}$; The complement is spinning yellow, blue, green, or purple.
7. 0.25, 25%, $\frac{1}{4}$