Every card in Probability, Year 8: more practice
The whole deck, in order — so you can read it through before your child ever sees it.
- A bag has 3 red, 5 blue and 2 green counters. What is the probability that a counter taken at random is blue?
1/2 (5 out of 10)
HintCount the favourable counters and all the counters.
WhyThere are 3 + 5 + 2 = 10 counters in all, and 5 are blue: 5/10 = 1/2.
- Two fair dice are rolled and their scores are added. How many of the 36 outcomes give a total of 7?
6
HintFix the first dice and find the second that makes 7.
Why(1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Seven is the most likely total.
- Two fair dice are rolled and added. What is the probability of a total of 4?
3/36 = 1/12
HintList the pairs that make 4 in a table of outcomes.
WhyThe pairs are (1,3), (2,2) and (3,1), so 3 outcomes out of 36. 3/36 = 1/12.
- P(win) = 0.35 and P(draw) = 0.25. What is P(lose)?
0.4
HintThe three probabilities must add up to 1.
Why1 − 0.35 − 0.25 = 0.4.
- Can 0.5, 0.3 and 0.4 be the probabilities of all the possible outcomes of a game? Say why.
No — they add up to 1.2, which is more than 1
HintAdd them together.
WhyThe probabilities of all the outcomes must total exactly 1. 0.5 + 0.3 + 0.4 = 1.2.
- A coin lands heads 36 times in 80 tosses. What is the experimental probability of heads, as a decimal?
0.45
HintExperimental probability = successes ÷ number of trials.
Why36 ÷ 80 = 0.45. This is an estimate: a different set of 80 tosses would give a slightly different answer.
- What is another name for the number of times an event happens divided by the number of trials?
Relative frequency
HintIt is the experimental probability.
WhyRelative frequency is the fraction of trials in which the event happened. It is often used to estimate probability when theory is not available.
- After many thousands of trials, a dice's experimental probability for a six is still far from 1/6. What does this suggest?
The dice may be biased
HintMany trials make random variation small.
WhyWith very large numbers of trials, the experimental probability should settle close to the theoretical value for a fair dice.
- As a fair dice is rolled more and more times, the proportion of sixes tends to settle near what value?
1/6
HintThis is the theoretical probability.
WhyThe more trials, the closer the experimental probability usually gets to the theoretical one. Short runs can be far off.
- The probability of rain on any day is 0.2. About how many rainy days are expected in 30 days? (number only)
6
HintExpected frequency = probability × number of trials.
Why0.2 × 30 = 6. It is an expected value, not a promise.
1★ KS3-MATH-PRB-0045
2★ KS3-MATH-PRB-0046
3★ KS3-MATH-PRB-0047
4★ KS3-MATH-PRB-0048
5★ KS3-MATH-PRB-0049
6★ KS3-MATH-PRB-0050
7★ KS3-MATH-PRB-0051
8★ KS3-MATH-PRB-0052
9★ KS3-MATH-PRB-0053
10★ KS3-MATH-PRB-0054
Keep what you learn
Here, nothing is saved. In your child’s own sky every card is scheduled — it comes back just before they’d forget it — and the professor who wrote it is one tap away.