Sample Space
A coin is flipped once. What is the sample space?
Answer: {H, T}
A fair coin is flipped twice. What is the probability of getting heads both times?
Answer: 1/2 x 1/2 = 1/4
A fair coin is flipped once. What is the theoretical probability of getting heads?
Answer: 1/2
A coin is flipped 20 times. Heads comes up 12 times. What is the experimental probability of getting heads?
Answer: 12/20 = 3/5
A spinner has 4 equal sections labeled 1–4. If the spinner is spun 100 times, about how many times will a 3 be expected?
1/4 × 100 = 25 times
A 6-sided die is rolled once. What is the sample space?
Answer: {1, 2, 3, 4, 5, 6}
A 6-sided die is rolled twice. What is the probability of rolling a 2 and then a 5?
Answer: 1/6 x 1/6 = 1/36
A 6-sided die is rolled once. What is the theoretical probability of rolling a number greater than 4?
Answer: 2/6 = 1/3
A die is rolled 30 times. The number 4 appears 6 times. What is the experimental probability of rolling a 4?
Answer: 6/30 = 1/5
A 6-sided die is rolled 120 times. About how many times will a number greater than 4 be expected?
Answer: 2/6 × 120 = 40 times
A spinner has 3 equal sections labeled A, B, and C. It is spun twice. What is the sample space?
Answer:
{AA, AB, AC, BA, BB, BC, CA, CB, CC}
A 6-sided die is rolled twice. What is the probability of rolling an even number first and then an odd number? Express your answer as a decimal.
Answer: 1/2 × 1/2 = 1/4 = .25
A bag contains 4 red marbles, 3 blue marbles, and 3 green marbles. What is the theoretical probability of randomly drawing a blue marble? Express your answer as a percent.
Answer: 3/10 = .3 = 30%
A spinner is spun 40 times. It lands on red 18 times, blue 12 times, and green 10 times. What is the experimental probability of landing on blue?
Answer: 12/40 = 3/10
A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If a marble is drawn (with replacement) 200 times, about how many times will a blue marble be expected?
Answer: 5/10 × 200 = 100 times
A coin is flipped and a 6-sided die is rolled. What is the total number of outcomes in the sample space?
Answer:
Coin outcomes: 2
Die outcomes:6
Total outcomes: 2 x 6 = 12
A fair 6-sided die is rolled, and then a coin is flipped. What is the probability of rolling a number greater than 4 and flipping heads?
Answer: 2/6 x 1/2 = 2/12 = 1/6
A spinner has 8 equal sections labeled 1 through 8. What is the theoretical probability of landing on a number that is a multiple of 3?
Answer: 2/8 = 1/4
A bag of marbles is tested by drawing a marble, recording the color, and replacing it each time. After 50 trials, a yellow marble was drawn 15 times. What is the experimental probability of drawing yellow?
Answer: 15/50 = 3/10
A spinner has 8 equal sections numbered 1–8. If it is spun 160 times, about how many times will a number less than 3 be expected?
Answer: 2/8 × 160 = 40 times
A coin is flipped twice and a 4-sided die (numbers 1–4) is rolled once. What is the total number of outcomes in the sample space?
Answer:
Coin outcomes: 2 × 2 = 4
Die outcomes: 4
Total outcomes: 4 × 4 = 16 outcomes
A number cube is rolled and a spinner with 4 equal sections (A, B, C, D) is spun. What is the probability of rolling a 3 or 4 and landing on C? Express your answer as a percent, rounded to the nearest whole number.
Answer: 2/6 x 1/4 = 2/24 = 1/12 = 8%
A jar contains 6 green marbles, 4 purple marbles, and 5 orange marbles. What is the theoretical probability of randomly drawing a marble that is not purple? Express your answer as a decimal, rounded to the nearest tenths place.
Answer:
Total marbles = 15
Not purple = 6 + 5 = 11
Probability = 11/15 = 0.7
A number cube is rolled 60 times. The results are:
What is the experimental probability of rolling a number greater than 4?
Answer:
Numbers greater than 4 → 5 and 6
11 + 10 = 21
Probability = 21/60 = 7/20
A bag contains 4 yellow marbles, 6 purple marbles, and 10 orange marbles. If a marble is drawn (with replacement) 300 times, about how many times will a marble that is not purple be expected?
Answer:
Not purple = 4 + 10 = 14 out of 20
14/20 × 300 = 210 times