4MA0 Higher January 2018 Paper 3 Q22
22 When a biased coin is thrown 5 times, the probability of getting 5 heads is \(\dfrac{32}{3125}\)
Work out the probability of getting 4 heads and 1 tail when the coin is thrown 5 times.
(3)
| Scheme | Marks |
|---|---|
| \(\sqrt[5]{\dfrac{32}{3125}}\left(= \dfrac{2}{5}\text{ oe}\right)\) | M1 |
| \(\left(\text{“}\dfrac{2}{5}\text{”}\right)^4 \times \left(1 - \text{“}\dfrac{2}{5}\text{”}\right)\) oe \(\left(= \dfrac{48}{3125}\text{ oe}\right)\) | M1 |
| \(\dfrac{240}{3125}\) | A1 |
| (3) |
Notes
M1: a correct method to find probability of getting one head
M1: (dep) for the probability of getting one combination of 4 heads and 1 tail
A1: oe eg \(\dfrac{48}{625}\), 0.0768