Higher June 2025 Paper 2 Q17
17 When a biased coin is spun, \(\quad\) P(Heads) : P(Tails) \(= 5 : 2\)
In a game, the player spins the coin four times.
The player can win in two ways.
| 1st way to win Spin 4 heads | 2nd way to win Spin a Head, then a Tail, then a Head, then a Tail |
How many times more likely is a player to win the 1st way than the 2nd way? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\left(\dfrac{5}{5 + 2}\right)^4\) or \(\left(\dfrac{5}{7}\right)^4\) or \(\dfrac{625}{2401}\) or \(\left(\dfrac{5}{7}\right)^2 \times \left(1 - \dfrac{5}{7}\right)^2\) or \(\left(\dfrac{5}{7}\right)^2 \times \left(\dfrac{2}{7}\right)^2\) or \(\dfrac{100}{2401}\) | M1 | oe eg \([0.71, 0.72]^4\) or [0.25, 0.27] or \([0.71, 0.72]^2 \times [0.28, 0.29]^2\) or [0.039, 0.044] |
| \(\left(\dfrac{5}{7}\right)^4 \div \left[\left(\dfrac{5}{7}\right)^2 \times \left(\dfrac{2}{7}\right)^2\right]\) or \(\dfrac{625}{2401} \div \dfrac{100}{2401}\) | M1dep | oe full method eg \([0.71, 0.72]^4 \div ([0.71, 0.72]^2 \times [0.28, 0.29]^2)\) or \([0.25, 0.27] \div [0.039, 0.044]\) |
| 6.25 or \(6\dfrac{1}{4}\) | A1 | oe value eg \(\dfrac{625}{100}\) |
Additional guidance
| Working in percentages can score up to 3 marks eg \([71, 72]^4\) or [25 000 000, 27 000 000] or \([71, 72]^2 \times [28, 29]^2\) or [3 900 000, 4 400 000] \([71, 72]^4 \div ([71, 72]^2 \times [28, 29]^2)\) 6.25 | M1 M1dep A1 |
| \(5^4\) or 625 or \(5^2 \times 2^2\) or 100 with no further correct working scores M0 but \(5^4 \div (5^2 \times 2^2)\) or \(625 \div 100\) scores M1M1 | |
| Missing brackets must be recovered |