Higher June 2018 Unit 1 Q17
17. At a children’s party, the children play a number of games.
The winner of each game chooses a ticket for a prize, at random, from a box.
The ticket is not returned to the box.
At the start of the party, there are 12 prizes available: 1 book, 3 key-rings and 8 pencils.
(a) Find the probability that the winners of the first two games choose the same type of prize. [3]
(b) After the winners of the first three games have chosen their prizes, find the probability that the ticket for the book is still in the box. [2]
| Scheme | Marks | Comments |
|---|---|---|
| Either 8/12 × 7/11 or 3/12 × 2/11 | B1 | |
| 8/12 × 7/11 + 3/12 × 2/11 with no incorrect additional terms | M1 | |
| 62/132 (=31/66) | A1 | ISW. If no other marks awarded, SC1 for an answer of 73/144 (from working ‘with replacement’, without allowing for 2 books) |
| Scheme | Marks | Comments |
|---|---|---|
| 11/12 × 10/11 × 9/10 or equivalent | M1 | Or P(PPP) + 3 × P(PPK) + 3 × P(PKK) + P(KKK) (or an alternative full method) |
| 990/1320 (= 3/4) or equivalent | A1 | ISW FT consistent use of ‘their 12 × 11’. If no other marks awarded, SC1 for an answer of 1331/1728 (from working ‘with replacement’) OR SC1 for this method and related answer, having omitted up to two (out of eight) products OR SC1 for 11/12 × 10/11 × 9/10 × 1/9 = 990/11880 (= 1/12) (for the 4th prize being the book) |