Practice: Probability

Part A: Sample Spaces

Directions: List all possible outcomes (sample space) for each experiment.

1. Flipping a coin twice.

Sample space: {________________________________}

Number of outcomes:

2. Rolling a die and recording whether it's even (E) or odd (O).

Sample space: {________________________________}

Number of outcomes:

3. Spinning a spinner with sections A, B, C and flipping a coin.

Sample space: {________________________________}

Number of outcomes:

Part B: Calculating Probability

Directions: Calculate each probability. Express as a fraction in lowest terms.

4. A bag contains 4 red, 6 blue, and 5 green marbles. Find:

a) P(red) =

b) P(blue) =

c) P(green) =

d) P(red or blue) =

e) P(not green) =

5. A spinner has 10 equal sections numbered 1-10. Find:

a) P(landing on 7) =

b) P(landing on even number) =

c) P(landing on number greater than 6) =

d) P(landing on number less than 11) =

6. A standard deck has 52 cards. P(drawing a King)?

Answer:

7. Same deck. P(drawing a red card)?

Answer:

Part C: Interpreting Probability

Directions: Classify each probability as impossible, unlikely, equally likely, likely, or certain.

8. P = 0

Classification: ________________

9. P = 0.85

Classification: ________________

10. P = 1/2

Classification: ________________

11. P = 1

Classification: ________________

Part D: Comparing Probabilities

Directions: Calculate probabilities and compare. Show your work.

12. Box A has 3 red and 7 blue balls. Box B has 5 red and 5 blue balls. From which box are you MORE likely to pick a red ball?

P(red from A) =

P(red from B) =

More likely: Box

13. Order these events from LEAST likely to MOST likely:

Event A: Rolling a 6 on a die (P = 1/6)

Event B: Flipping heads (P = 1/2)

Event C: Picking a red marble from a bag of 8 red and 2 blue (P = 8/10)

Order (least to most): _______ , _______ , _______

Part E: Word Problems

Directions: Read each problem carefully. Show your work.

14. A basketball player makes 7 out of 10 free throws. What is the probability she will make her next free throw? Express as a fraction, decimal, and percent.

Fraction: Decimal: Percent:

15. A weather forecast says there's a 30% chance of rain. What is the probability it will NOT rain? Express as a fraction and decimal.

P(no rain) as fraction: as decimal:

16. In a class of 30 students, 18 are girls. If a student is chosen at random, what is the probability of choosing a boy?

P(boy) =

Part F: Tree Diagrams

Directions: Complete the tree diagram and use it to find probabilities.

17. You flip a coin and then roll a die. Complete the tree diagram.

Start with Coin: Heads (H) or Tails (T)
Then Die: 1, 2, 3, 4, 5, or 6 for each coin outcome

a) How many outcomes in the sample space?

b) P(Heads and 4) =

c) P(Tails and even number) =

Challenge: Compound Events

18. A bag has 3 red and 2 blue marbles. You pick one marble, put it back, then pick another. What is the probability of picking red BOTH times?

(Hint: For independent events, multiply the probabilities)

P(red then red) =

19. Using the same bag (3 red, 2 blue), what is the probability of picking at least one blue marble in two picks (with replacement)?

(Hint: P(at least one blue) = 1 - P(no blue) = 1 - P(red then red))

P(at least one blue) =