Year 11 Probability Practice

Name:

Date:

Part 1: Reference and Quick Checks

Key formulas

For equally likely outcomes: P(A) = favourable outcomes ÷ total outcomes

P(not A) = 1 − P(A)

Expected frequency = number of trials × probability

For independent two-step events, multiply the probabilities along a branch. Add the probabilities of branches that give the required outcome.

1. A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

1/6

1/3

1/2

2/3

2. The probability that a bus is on time is 0.82. What is the probability that it is late?

0.08

0.18

0.28

1.82

3. A coin is tossed 200 times and lands on heads 116 times. What is the experimental probability of heads?

0.42

0.50

0.58

1.16

Part 2: Probability Problems

4. A bag contains 5 red, 3 blue and 2 green counters. One counter is selected at random. Find the probability of selecting:

a) a blue counter: _________

b) a counter that is not green: _________

5. A fair spinner has four equal sections labelled A, B, C and D. It is spun twice. Complete a tree diagram and use it to find the probability of getting two letters that are the same.

Probability: _________

6. A school surveys 150 students about how they travel to school. The probability that a randomly selected student walks is 0.24. What is the expected number of students who walk?

7. At a Wellington bus stop, a student records whether the bus arrives on time over 80 mornings. It arrives on time 68 times.

a) Calculate the experimental probability of an on-time arrival.

b) The transport company states that the theoretical probability of an on-time arrival is 0.80. Compare the two probabilities and explain the difference.

8. A box contains 4 chocolate and 6 plain biscuits. Two biscuits are selected without replacement. Find the probability that both biscuits are chocolate.

9. A New Zealand conservation group estimates that the probability of spotting a kiwi on one night walk is 0.30. On three independent night walks, find the probability of:

a) spotting a kiwi on all three walks: _________

b) spotting a kiwi on at least one walk: _________

Part 3: Answer Key

1. 1/3

2. 0.18

3. 116 ÷ 200 = 0.58

4. a) 3/10 b) 8/10 = 4/5

5. There are 16 equally likely two-spin outcomes. Four have matching letters: AA, BB, CC and DD. Probability = 4/16 = 1/4.

6. 150 × 0.24 = 36 students

7. a) 68/80 = 0.85. b) The experimental probability is 0.05 higher than the theoretical probability. This difference is due to natural variation in a limited number of observations.

8. (4/10) × (3/9) = 12/90 = 2/15

9. a) 0.30 × 0.30 × 0.30 = 0.027. b) P(at least one) = 1 − P(none) = 1 − (0.70 × 0.70 × 0.70) = 0.657.