Probability, Year 7: more practice

Impossible

提示Look at the numbers on the faces.

为什么There is no 7, so the probability is 0. The word is impossible, not just unlikely.

An even number

提示Count how many faces give each result.

为什么Even numbers: 2, 4, 6 — three faces. Numbers greater than 4: 5, 6 — two faces. So even is more likely.

1

提示Think about the right-hand end of the probability scale.

为什么Every probability lies between 0 (impossible) and 1 (certain). A probability can never be more than 1.

3/5

提示Change both to decimals first.

为什么3/5 = 0.6, which is greater than 0.4.

HH, HT, TH, TT

提示Fix the first flip, then list both possibilities for the second.

为什么Each flip has two results. Taking the first flip in order gives HH, HT, then TH, TT, so four outcomes. HT and TH are different outcomes.

8

提示Each flip doubles the number of outcomes so far.

为什么2 × 2 × 2 = 8. List them systematically to check: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

9

提示There are three choices for the tens digit and three for the units digit.

为什么The tens digit can be 1, 2 or 3, and for each there are three choices for the units: 3 × 3 = 9.

47, 49, 74, 79, 94, 97

提示Start with each tens digit in turn.

为什么Starting with 4: 47, 49. With 7: 74, 79. With 9: 94, 97. Six numbers in all, 3 × 2 = 6.

1/5

提示Fair means every section is equally likely.

为什么The five equal probabilities must add up to 1, so each is 1/5.

No — I win with probability 1/6 and you win with 5/6

提示Compare the chance each player has of winning.

为什么A fair game needs both players to have the same chance. Here one player has 5 faces and the other only one.