Higher June 2018 Paper 1 Q19
19 Jack plays a game with two fair spinners, A and B.
Spinner A can land on the number 2 or 3 or 5 or 7
Spinner B can land on the number 2 or 3 or 4 or 5 or 6
Jack spins both spinners.
He wins the game if one spinner lands on an odd number and the other spinner lands on an even number.
Jack plays the game twice.
Work out the probability that Jack wins the game both times.
(4)
| Scheme | Marks |
|---|---|
\(\dfrac{1}{4} \times \dfrac{2}{5} \left(= \dfrac{2}{20}\right)\) or \(\dfrac{3}{4} \times \dfrac{3}{5} \left(= \dfrac{9}{20}\right)\) or \(\dfrac{1}{4} \times \dfrac{3}{5} \left(= \dfrac{3}{20}\right)\) or \(\dfrac{3}{4} \times \dfrac{2}{5} \left(= \dfrac{6}{20}\right)\) | M1 |
| \(\dfrac{1}{4} \times \dfrac{2}{5} + \dfrac{3}{4} \times \dfrac{3}{5} \left(= \dfrac{11}{20}\right)\) or \(1 - \left(\dfrac{1}{4} \times \dfrac{3}{5} + \dfrac{3}{4} \times \dfrac{2}{5}\right) \left(= \dfrac{11}{20}\right)\) | M1 |
| \(\text{``}{\dfrac{11}{20}}\text{''} \times \text{``}{\dfrac{11}{20}}\text{''}\) or \(\left(\text{``}{\dfrac{2}{20}}\text{''} + \text{``}{\dfrac{9}{20}}\text{''}\right)^2\) | M1 |
| \(\dfrac{121}{400}\) oe | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for any one correct probability
M1: for a complete method
A1: for \(\dfrac{121}{400}\) oe or 0.3025 or 30.25%