ExpertEasy1 markMultiple Choice
AQA GCSE · Question 01 · Statistical Measures and Calculations
Two fair spinners, each numbered 1 to 8, are spun. The numbers they land on are added up. What is the probability the total is 16?
Two fair spinners, each numbered 1 to 8, are spun. The numbers they land on are added up. What is the probability the total is 16?
Answer options:
A.
1/4
B.
1/16
C.
1/32
D.
1/64
How to approach this question
1. Identify the total number of outcomes for each spinner (8).
2. Determine the specific outcome needed on each spinner to achieve the target total (16). The only combination is 8 + 8.
3. Calculate the probability of this outcome for one spinner (P(8) = 1/8).
4. Since the spinners are independent, multiply the probabilities for each spinner to get the combined probability: P(8 and 8) = P(8) * P(8).
5. Calculate the final answer: 1/8 * 1/8 = 1/64.
Full Answer
D.1/64✓ Correct
This question tests the concept of probability for two independent events. The highest possible score on one spinner is 8. To get a total of 16, both spinners must land on 8. The probability of one fair 8-sided spinner landing on 8 is 1/8. Since the two spins are independent events, the probability of both events happening is the product of their individual probabilities. Therefore, the probability of getting an 8 on the first spinner AND an 8 on the second spinner is (1/8) × (1/8) = 1/64.
Common mistakes
✗ Adding the probabilities (1/8 + 1/8 = 2/8 = 1/4). You must multiply probabilities for independent 'AND' events.
✗ Thinking there are two ways to get 16 (e.g., spinner 1 is 8, spinner 2 is 8 and vice versa), but this is the same single outcome.
✗ Incorrectly calculating the product, e.g., 8 * 8 = 16.
Practice the full AQA GCSE Statistics Higher Tier Paper 1
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