Higher June 2023 Paper 1 Q12
12 Martha plays a game twice.
The probability tree diagram shows the probabilities that Martha will win or lose each game.
Find the probability that Martha will lose at least one game. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{62}{72}\) | M1 | for one correct product, eg \(\dfrac{5}{8} \times \dfrac{7}{9}\ \left(= \dfrac{35}{72}\right)\) oe or \(\dfrac{3}{8} \times \dfrac{2}{9}\ \left(= \dfrac{6}{72}\right)\) oe or \(\dfrac{3}{8} \times \dfrac{7}{9}\ \left(= \dfrac{21}{72}\right)\) oe or \(\dfrac{5}{8} \times \dfrac{2}{9}\ \left(= \dfrac{10}{72}\right)\) oe |
| M1 | for a full method, eg \(\dfrac{5}{8} \times \dfrac{7}{9} + \dfrac{3}{8} \times \dfrac{2}{9} + \dfrac{3}{8} \times \dfrac{7}{9}\) oe or \(1 - \dfrac{5}{8} \times \dfrac{2}{9}\) oe | |
| A1 | for \(\dfrac{62}{72}\) oe eg \(\dfrac{31}{36}\) |