Higher June 2022 Paper 2R Q14
14 Ciara throws four fair six-sided dice.
The faces of each dice are labelled with the numbers 1, 2, 3, 4, 5, 6
Work out the probability that at least one of the dice lands on an even number.
(3)
| Scheme | Marks |
|---|---|
eg \(\left(\dfrac{1}{2}\right)^4\left(= \dfrac{1}{16}\text{ or }0.0625\right)\) or \(4\left(\dfrac{1}{2}\right)^4\left(= \dfrac{4}{16}\text{ or }\dfrac{1}{4}\text{ or }0.25\right)\) or \(6\left(\dfrac{1}{2}\right)^4\left(= \dfrac{6}{16}\text{ or }\dfrac{3}{8}\text{ or }0.375\right)\) oe | M1 |
eg \(1 - \left(\dfrac{1}{2}\right)^4\) or \(4\left(\dfrac{1}{2}\right)^4 + 6\left(\dfrac{1}{2}\right)^4 + 4\left(\dfrac{1}{2}\right)^4 + \left(\dfrac{1}{2}\right)^4\) or (e + oe + ooe + oooe) \(\dfrac{1}{2} + \dfrac{1}{2} \times \dfrac{1}{2} + \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} + \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}\) \(\left(= \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{16}\right)\) oe | M1 |
| \(\dfrac{15}{16}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for finding the probability of one correct combination eg calculation for oooo or eeee or 4 × eooo or 4 × eeeo or 6 × eeoo
M1: for a complete method
A1: oe eg 0.9375
(allow 0.937 or 0.938)