Probability Basics
What is the probability of flipping a fair coin and getting heads?
1/2 (or 50%)
What is theoretical probability?
Theoretical probability is the expected likelihood of an event occurring, based on all possible outcomes.
A probability of 0 means an event is ___.
Impossible
What is experimental probability?
Experimental probability is the ratio of the number of times an event occurs to the total number of trials in an actual experiment.
If the weather forecast says there is a 70% chance of rain, is it likely, unlikely, or neither?
Likely
Probability is always a number between __ and __.
0 and 1
If a spinner has 8 equal sections numbered 1-8, what is the probability of landing on an even number?
4/8 = 1/2 (or 50%)
A probability of 1 means an event is ___.
Certain
If you flip a coin 50 times and it lands on heads 28 times, what is the experimental probability of getting heads?
28/50 = 14/25 (or 56%)
If a lottery ticket has a 1 in 10,000 chance of winning, is winning likely or unlikely?
Unlikely
What is the probability of rolling a standard six-sided die and getting a number greater than 4?
2/6 = 1/3 (or about 33.3%)
If you draw a card from a standard deck of 52, what is the probability of drawing an ace?
4/52 = 1/13 (or about 7.7%)
A probability of 1/2 means an event is ___.
Equally likely to happen or not happen
If a spinner lands on red 40 out of 100 spins, what is the experimental probability of landing on red?
2/5 (or 40%)
If a sports team wins 60% of their games, how many games would you expect them to win out of 50?
60% of 50 = 0.6 × 50 = 30 games
If you randomly pick a letter from the word "MATH," what is the probability of picking a vowel?
1/4 (since "MATH" has 4 letters, and only "A" is a vowel)
A box contains 2 yellow, 3 green, and 5 blue balls. What is the probability of drawing a green ball?
3/10 (or 30%)
Which event is more likely: rolling a 3 on a standard die or flipping heads on a coin?
Flipping heads on a coin (1/2 or 50%) is more likely than rolling a 3 on a die (1/6 or about 16.7%).
A number cube is rolled 500 times, and a 2 is rolled 90 times. How does the experimental probability compare to the theoretical probability?
The theoretical probability of rolling a 2 is 1/6 (≈16.7%), while the experimental probability is 90/500 = 18%. The experimental probability is close but not exact due to randomness in trials.
A store finds that 15 out of 100 customers buy a certain product. What is the probability that the next customer buys the product?
15/100 = 3/20 (or 15%)
A bag contains 3 red, 4 blue, and 5 green marbles. What is the probability of randomly picking a red marble?
3/12 = 1/4 (or 25%)
A number cube is rolled 300 times. How many times would you expect to roll a 5?
1/6 × 300 = 50 times
Which event is less likely: drawing a red card from a standard deck or rolling a 6 on a six-sided die?
Rolling a 6 on a six-sided die (1/6 or about 16.7%) is less likely than drawing a red card from a deck (26/52 = 1/2 or 50%)
Why might experimental probability be different from theoretical probability?
Experimental probability may differ from theoretical probability due to randomness, small sample size, or external factors affecting outcomes.
Why do insurance companies use probability in their business?
Insurance companies use probability to assess risks, set premiums, and predict future claims based on data and statistics.