4400 Higher June 2005 Paper 3 Q19
19 The diagram shows six counters.
Each counter has a letter on it.
Bishen puts the six counters into a bag.
He takes a counter at random from the bag.
He records the letter which is on the counter and replaces the counter in the bag.
He then takes a second counter at random and records the letter which is on the counter.
(a) Calculate the probability that the first letter will be A and the second letter will be N. (2)
(b) Calculate the probability that both letters will be the same. (4)
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{6} \times \dfrac{2}{6}\) | M1 |
| \(\dfrac{6}{36}\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(\dfrac{1}{6} \times \dfrac{1}{6} + \dfrac{3}{6} \times \dfrac{3}{6} + \dfrac{2}{6} \times \dfrac{2}{6}\) \(= \dfrac{1}{36} + \dfrac{9}{36} + \dfrac{4}{36}\) | M1 M1 M1 |
| \(\dfrac{14}{36}\) | A1 |
| (4) | |
| (6 marks) |
Notes
M1: 1 correct product
M1: All 3 correct products
M1: Summing at least 2 correct products
Alternative
| BB BA BN BA BN BA AB AA AN AA AN AA NB NA NN NA NN NA AB AA AN AA AN AA NB NA NN NA NN NA AB AA AN AA AN AA | M3 |
| \(\dfrac{14}{36}\) | A1 |
M3: List of all 36 combinations
M2 for 1 omission
M1 for 15 or more combinations