Foundation November 2020 Paper 2 Q8
8. A set of raffle tickets numbered 1 to 500 are all sold at a charity event.
A ticket, picked at random, wins the only prize.
(a) What is the probability that the number on the winning ticket is 20? [1]
(b) What is the probability that the number on the winning ticket is greater than 200? [1]
(c)
Ben has bought 8 of the tickets.
He says,
“I have a 50% chance of winning because either I win or I don’t win.”
Is Ben correct?
Yes ☐ No ☐
Explain your answer. [1]
(d)
The probability that Zac wins the prize is 0.01.
(i) What is the probability that Zac does not win the prize? [1]
(ii) How many raffle tickets does Zac have? [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{1}{500}\) oe | B1 | ISW Do not accept incorrect notation e.g ‘1 out of 500’ |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{300}{500}\) or 0.6 oe | B1 | ISW Do not accept incorrect notation e.g ‘300 out of 500’ NOTE: If no marks awarded in (a) or (b) award SC1 for consistent incorrect notation e.g ‘1 out of 500’ AND ‘300 out of 500’. |
| Scheme | Marks | Comments |
|---|---|---|
| No and a correct explanation e.g. ‘The probability is \(\dfrac{8}{500}\) (so less than 50%)’ ‘He has less than half the tickets so less than 50% chance.’ ‘He would have to buy 250 tickets to have a 50% chance of winning.’ | E1 | Allow e.g. ‘Ben winning and losing are not equally likely.’ ‘He will have an 8 in 500 chance of winning.’ ‘He needs more tickets to have a 50% chance.’ ‘He hasn’t bought 50% of the tickets.’ Do not allow e.g. ‘Winning and losing are not equally likely.’ ‘he only has 8 out of 500 tickets’ |
| Scheme | Marks | Comments |
|---|---|---|
| (i) 0.99 oe | B1 | |
| (ii) 0.01 × 500 or 500 – (0.99 × 500) | M1 | Accept \(\left(\dfrac{1}{100} =\right) \dfrac{5}{500}\) for M1 |
| = 5 (tickets) | A1 | |
| (6) |