Probability, Year 8: more practice：全部卡片
整套按顺序列出——孩子看到之前，您可以先通读一遍。
- 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)
提示Count the favourable counters and all the counters.
为什么There 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
提示Fix the first dice and find the second that makes 7.
为什么(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
提示List the pairs that make 4 in a table of outcomes.
为什么The 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
提示The three probabilities must add up to 1.
为什么1 − 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
提示Add them together.
为什么The 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
提示Experimental probability = successes ÷ number of trials.
为什么36 ÷ 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
提示It is the experimental probability.
为什么Relative 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
提示Many trials make random variation small.
为什么With 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
提示This is the theoretical probability.
为什么The 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
提示Expected frequency = probability × number of trials.
为什么0.2 × 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