Foundation June 2019 Paper 3 Q20
20 Sophie is organising a raffle.
- Each raffle ticket costs 50p.
- She sells 400 tickets.
- The probability that a ticket, chosen at random, wins a prize is 0.1.
- Each winning ticket receives a prize worth £3.
Sophie says
I expect the raffle to make over £100 profit.
Show that Sophie is wrong. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [expected profit is £] 80 with 200 and 120 seen | 4 | B1 for [£] 200 or 20 000[p] AND M2 for \(0.1 \times 400 \times 3\) soi 120 or M1 for \(0.1 \times 400\) soi 40 Alternative method B1 for [£] 200 or 20 000[p] M1 for \(\dfrac{\text{their } 200 - 100}{3}\) [prizes] soi 33[.3…] M1 for \(0.1 \times 400\) soi 40 A1 for she is giving away too many prizes oe Alternative method B1 for [£] 200 or 20 000[p] M1 for \(\dfrac{\text{their } 200 - 100}{3}\) [prizes] soi 33[.3…] M1 for \(\dfrac{\text{their } 33[.3...]}{400}\) soi 0.08[3…] A1 for the probability of winning the game is too great oe | Apply scheme to consistent working in pence rather than £. |