Grade 8 Probability — Answer Key

Teacher:

Date:

🎯 Success Criteria

By the end of this lesson, students should be able to:

✅ Express probability as a fraction, decimal, and percentage

✅ Identify complementary events and use P(A') = 1 − P(A)

✅ Construct and interpret sample spaces for two-step experiments

✅ Calculate theoretical probability and compare to experimental results

✅ Use tree diagrams and tables to find probabilities of compound events

📚 Part 1: Multiple Choice — Answers

1. A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of picking a blue marble?

A) 1/2

B) 3/10

C) 1/2 ✅ → 5/10 = 1/2

D) 2/5

2. If P(rain tomorrow) = 0.35, what is the probability it will NOT rain?

A) 0.35

B) 0.65 ✅ → 1 − 0.35 = 0.65

C) 0.70

D) 1.35

3. A fair die is rolled. What is the probability of rolling a number greater than 4?

A) 1/6

B) 1/3

C) 1/3 ✅ → Outcomes {5, 6} = 2/6 = 1/3

D) 2/3

4. Two coins are tossed. How many outcomes are in the sample space?

A) 2

B) 3

C) 4 ✅ → {HH, HT, TH, TT}

D) 6

5. A spinner has 8 equal sections numbered 1–8. What is P(even number)?

A) 1/4

B) 3/8

C) 1/2 ✅ → Even: {2,4,6,8} = 4/8 = 1/2

D) 5/8

✏️ Part 2: Short Answer — Answers

6. A class of 25 students has 10 boys and 15 girls. One student is chosen at random. Find P(girl) as a fraction, decimal, and percentage.

✅ Answer: P(girl) = 15/25 = 3/5 = 0.6 = 60%

7. A card is drawn from a standard deck of 52 cards. Find the probability of drawing a heart OR a king. (Note: King of hearts counts once.)

✅ Answer: P(heart) = 13/52, P(king) = 4/52, P(king of hearts) = 1/52

P(heart OR king) = 13/52 + 4/52 − 1/52 = 16/52 = 4/13

8. A coin is flipped and a die is rolled. Complete the sample space table and find P(Heads and an odd number).

✅ Sample Space (12 outcomes):

H1, H2, H3, H4, H5, H6 | T1, T2, T3, T4, T5, T6

P(Heads AND odd) = 3/12 = 1/4 → Favourable: {H1, H3, H5}

9. In an experiment, a die was rolled 60 times. A "3" appeared 14 times.
(a) What is the experimental probability of rolling a 3?
(b) How does this compare to the theoretical probability?

✅ (a) Experimental P(3) = 14/60 = 7/30 ≈ 0.233 (23.3%)

✅ (b) Theoretical P(3) = 1/6 ≈ 0.167 (16.7%). The experimental result is slightly higher. With more trials, the experimental probability should get closer to 1/6 (Law of Large Numbers).

10. A school canteen sells pies and rolls. On Monday, 18 out of 30 students chose a pie. Estimate the probability that the next student chooses a roll.

✅ Answer: P(pie) = 18/30 = 3/5 → P(roll) = 1 − 3/5 = 2/5 = 0.4 = 40%

🌟 Extension Activity — Advanced Learners

For students working beyond the standard level (ICAS / Maths Olympiad preparation):

11. (Extension) Two dice are rolled. Find the probability that the sum of the two dice is a prime number. Show your working using a table or tree diagram.

✅ Answer: Total outcomes = 36. Sums that are prime: 2 (1 way), 3 (2 ways), 5 (4 ways), 7 (6 ways), 11 (2 ways) = 15 favourable outcomes.

P(prime sum) = 15/36 = 5/12

12. (Extension — Selective School Level) A bag contains 4 red and 3 blue balls. Two balls are drawn WITHOUT replacement. Find the probability that both balls are the same colour.

✅ Answer:

P(both red) = 4/7 × 3/6 = 12/42 = 2/7

P(both blue) = 3/7 × 2/6 = 6/42 = 1/7

P(same colour) = 2/7 + 1/7 = 3/7