Probability, Year 7: more practice

Impossible

HintLook at the numbers on the faces.

The whyThere is no 7, so the probability is 0. The word is impossible, not just unlikely.

An even number

HintCount how many faces give each result.

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

1

HintThink about the right-hand end of the probability scale.

The whyEvery probability lies between 0 (impossible) and 1 (certain). A probability can never be more than 1.

3/5

HintChange both to decimals first.

The why3/5 = 0.6, which is greater than 0.4.

HH, HT, TH, TT

HintFix the first flip, then list both possibilities for the second.

The whyEach 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

HintEach flip doubles the number of outcomes so far.

The why2 × 2 × 2 = 8. List them systematically to check: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

9

HintThere are three choices for the tens digit and three for the units digit.

The whyThe 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

HintStart with each tens digit in turn.

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

1/5

HintFair means every section is equally likely.

The whyThe 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

HintCompare the chance each player has of winning.

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