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Grade 8 Probability Mastery

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Grade 8 Probability Mastery

A community festival is testing games before opening day. Use probability to check outcomes, compare chances and recommend fair rules. Assume every coin, die and spinner is fair. Give probabilities as simplified fractions unless a question asks otherwise. Show working for multi-step problems.

Map the outcomes

Start by organising the possible results of the festival games.

1.A guest flips a coin and rolls a standard six-sided die numbered 1–6. How many equally likely outcomes are there altogether?

2.For the coin-and-die game, find the probability of getting tails and a number greater than 4. Show how you count the favourable outcomes.

3.Two fair six-sided dice are rolled. The grid shows the sum for each ordered pair of results. Use it to find the probability that the sum is 7.

Die 1 ↓ / Die 2 →

4.A fair spinner has four equal sectors labelled 1, 2, 3 and 4. It is spun twice. What is the probability that the total is at least 6? List or organise the successful pairs.

Read the festival survey

Organisers asked 80 visitors which activity they would try first. Each person chose one activity.

Visitors

Ring toss

Lucky dip

Total

Under 13

13 or over

Total

5.One visitor is chosen at random. Find the probability that they are under 13 and chose the lucky dip.

6.Given that a visitor is 13 or over, what is the probability they chose ring toss?

7.Are age group and activity choice independent in this survey? Compare the probability of choosing ring toss for under-13 visitors with the probability for all visitors, and explain.

Sort the prize tokens

A box has 20 tokens numbered 1 to 20. A token is drawn at random. Let A be the event ‘number is a multiple of 3’ and B be the event ‘number is a multiple of 4’.

8.List the numbers in A, the numbers in B, and the numbers in both sets. Then find P(A or B).

9.Using the same token box, find the probability of drawing a number that is in neither A nor B. Explain how you use the complement.

Check the games

Use complements and expected frequency to help the organisers choose sensible rules.

10.A player flips a fair coin four times. Find the probability of getting at least one head. Use the complement event in your working.

11.A die is rolled twice. What is the probability of getting at least one 6?

12.A prize game uses a fair six-sided die. The organisers expect 240 plays. How many times should they expect a roll of 5? State that this is an expected number, not a guarantee.

13.A bag contains 3 red, 4 blue and 5 yellow tokens. Two tokens are drawn without replacement. Find the probability that both are blue.