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Grade 8 Probability Practice

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Grade 8 Probability Practice

Show working for calculations. Give answers in simplest form where possible. For decimal answers, use exact values unless rounding is requested.

Probability foundations

Use favourable outcomes ÷ total possible outcomes for theoretical probability. Probability ranges from 0 (impossible) to 1 (certain).

Multiple choice

Choose the best answer for each question.

1.A pouch contains 5 black, 4 white and 3 orange counters. What is the probability of choosing a white counter?

1/3
1/4
4/9
5/12

2.A fair six-sided die is rolled. What is the probability of rolling a number less than 3?

3.If P(E) = 0.28, what is the probability that E does not occur?

0.28
0.62
0.72
1.28

4.A coin is tossed and a four-sided spinner numbered 1 to 4 is spun. How many outcomes are in the combined sample space?

5.Events C and D cannot happen on the same trial. If P(C) = 0.25 and P(D) = 0.45, find P(C or D).

0.1125
0.20
0.70
1.00

6.An equally divided spinner is labelled 1 to 10. What is the probability it stops on a multiple of 3?

1/10
3/10
1/2
7/10

7.One card is drawn from a standard 52-card deck. What is the probability of drawing a diamond or a queen?

4/13
15/52
17/52
1/4

8.A die is rolled 50 times and shows 5 on 9 of those rolls. What is the experimental probability of rolling a 5?

1/6
9/50
9/60
5/50

9.A token is drawn from a bag and kept out before a second token is drawn. How does the first draw affect the probability on the second draw?

The draws are independent
The draws are dependent
The draws are mutually exclusive
The draws are complementary

10.Two fair coins are tossed. What is the probability of getting two different results?

11.Events F and G are independent, with P(F) = 0.6 and P(G) = 0.3. Find P(F and G).

0.18
0.30
0.60
0.90

12.At a year-level survey, 14 students read the class newspaper, 11 contribute to its online poll, and 5 do both. Out of 30 students, what is the probability a randomly selected student reads the newspaper or contributes to the poll?

20/30
25/30
14/30
5/30

Short answer

Work through each situation and show your reasoning.

13.A box has 5 lemon, 3 berry and 4 mint sweets. Find P(lemon), P(not berry), P(lemon or mint), and express P(berry) as a decimal and percentage.

14.A fair die numbered 1 to 6 is rolled. Write the sample space, then find the probability of rolling an even number, a divisor of 6, and a number greater than 1 but less than 5.

15.In a survey of 180 students, 72 chose podcasts and 63 chose music as their preferred way to relax. Everyone else chose reading. Find the probability a student chooses reading, does not choose music, and chooses podcasts or music.

16.A local forecast gives a 2/9 chance of rain on a particular day. Find the probability of no rain that day.

17.A survey of 48 students recorded whether they prefer a news podcast or a printed class newspaper. The counts are: boys—podcast 13, newspaper 9; girls—podcast 11, newspaper 15. Complete the two-way table with row and column totals. Then find the probabilities that a randomly chosen student is (i) a girl who prefers the podcast, (ii) a student who prefers the newspaper, and (iii) a boy.

Group

Podcast

Newspaper

Total

Boys

Girls

Total

18.Grace tosses a coin 30 times and gets heads 17 times. State the experimental probability of heads and the theoretical probability. Explain why the results may differ.

19.For a single draw from a standard deck, decide whether each pair is mutually exclusive: (a) drawing a jack and drawing a 10; (b) drawing a spade and drawing a jack; (c) drawing a red card and drawing a black card. Give a reason for each.

20.A fair spinner has equal sections numbered 1 to 4. It is spun once and a fair coin is tossed. Find the probability of (a) spinning 2 and getting tails; (b) spinning an odd number and getting heads; (c) spinning a number greater than 2 and getting tails.

21.A container holds 6 red and 4 blue counters. Two counters are drawn without replacement. Find the probability the first is blue, the probability the second is red given the first was red, and the probability both are red.

22.A student has two independent quizzes. The probability of passing each is 0.8. Draw a tree diagram and calculate the probability of passing both, failing both, and passing exactly one.

23.Two fair dice are rolled. Use a 6 by 6 outcome table to help find the probability that the total is 8, the total is at least 11, both dice match, and the total is odd.

24.In a group of 32 students, 18 read the class newspaper, 14 listen to its audio edition, and 6 do both. Find the probability a student reads only the newspaper, reads or listens to either edition, and does neither.

25.The chance of rain on Friday is 40%, and on Saturday it is 30%. Assume the weather events are independent. Calculate the probability of rain both days, no rain on either day, and rain on at least one day.

26.A class newspaper team records 72 reader votes: 18 for a sports report, 24 for a book review, 12 for a science story and 18 for a local-news story. Give each category's relative frequency. If another 240 votes are expected, estimate how many will be for the book review. Find the experimental probability of a vote not being for science.

27.Among 36 students, 21 read French articles, 15 read Japanese articles, and 7 read both. If a French-article reader is selected, what is the probability they also read Japanese articles?

28.A charity raffle sells 600 tickets. Amira buys 9 and Anh buys 15, and no ticket has both names on it. Find the probability Amira wins, Anh wins, neither wins, and one of them wins.

29.Three different fair coins are tossed. List all eight outcomes using H and T, then find the probability of all heads, at least two tails, and exactly two heads.

30.A game combines an equally divided spinner with five colours, including blue, and a bag containing four numbered tiles, 1 to 4. A player wins by spinning blue and drawing tile 3. Give the chance of winning as a fraction, decimal and percentage.

Problem solving

Apply probability to practical situations. Show calculations and explain your conclusions when asked.

31.A manufacturer finds that 5 in every 250 rechargeable batteries fail inspection. If a retailer receives 1,200 batteries, how many would be expected to fail?

32.A square target is 60 cm by 60 cm. A circle of radius 15 cm is centred on it. If a dart is equally likely to land anywhere on the square, estimate the probability it lands in the circle. Use π≈3.14 and round to 3 decimal places.

33.A drawer contains 5 navy, 3 grey and 2 white socks. Two socks are drawn without replacement. Find the probability both are navy, one is navy and one is white, and neither is grey.

34.At a school, 3/8 of students cycle to school and 1/5 walk. The rest travel by bus. Find the fraction who travel by bus and the probability a randomly selected student cycles or walks. If there are 80 students, how many would be expected to travel by bus?

35.Spinner A has equally likely results 1, 2, 3 and 4. Spinner B has equally likely letters A, B and C. Find the number of combined outcomes, list those with A-spinner result 3, and calculate the probability of an even number with letter B.

36.The class newspaper team tracked whether its daily edition was published on 8 school days: it was published on 6 days and missed on 2. Find the experimental probability of publication and estimate how many publications there would be over the next 24 school days at the same rate. Is the experimental result guaranteed to equal the theoretical probability? Explain.

37.A bag contains 7 green and 5 orange counters. A counter is drawn, replaced, and then another is drawn. Find the probability of two greens, green then orange, and at least one orange. Explain whether the draws are independent.

38.At a school fete, 12% of players are expected to win a small prize. If 75 people play, estimate how many will win.

39.After six consecutive tails on a fair coin, a player says the next toss is more likely to be heads. Is this reasoning correct? Use probability to explain.

40.Grace wants to investigate whether a five-section spinner is fair. What is the theoretical probability of each number? Suggest a reasonable number of trials. If the spinner shows 4 on 28 out of 100 spins, what should Grace conclude?

Challenge

These final problems extend the probability ideas practised above.

41.In a group of 120 students, 72 take part in a sport. Of those, 45 bring a healthy lunch. Of the students who do not take part in a sport, 18 bring a healthy lunch. A student who brings a healthy lunch is chosen at random. Find the probability this student takes part in a sport. Show a suitable table or tree diagram.

42.A group of 4 students is selected from 6 boys and 5 girls. What is the probability the group includes exactly 2 girls?

43.A game costs $3 to play. On a fair die roll, a 6 wins $12, a 4 or 5 wins $4, and 1, 2 or 3 wins nothing. Calculate the expected prize and the expected net gain or loss after paying to play. Is the game favourable to the player?

44.A netballer makes 3/4 of her shots. Assuming each shot is independent, find the probability she makes all 3 of her next shots, misses all 3, and makes exactly 2 of the 3.