Sally plays two games against Martin - Edexcel - GCSE Maths - Question 15 - 2020 - Paper 1

To determine the probability that Sally wins exactly one of the two games, we need to consider the possible outcomes:

1. Sally wins the first game and loses the second:

   • The probability of Sally winning the first game is 0.3.

   • The probability of losing the second game can be calculated by subtracting the probabilities of winning and drawing from 1:

     $P(Lose) = 1 - P(Win) - P(Draw) = 1 - 0.3 - 0.1 = 0.6$

   • So, the probability for this outcome is:

     $P(Win ext{ first}, Lose ext{ second}) = 0.3 imes 0.6 = 0.18$

2. Sally loses the first game and wins the second:

   • The probability of losing the first game is 0.6 (as calculated above).

   • The probability of Sally winning the second game remains 0.3.

   • The probability for this outcome is:

     $P(Lose ext{ first}, Win ext{ second}) = 0.6 imes 0.3 = 0.18$

Now, to find the total probability that Sally wins exactly one of the two games, we sum the probabilities of the two scenarios we considered:

$P(Exactly ext{ one win}) = P(Win ext{ first}, Lose ext{ second}) + P(Lose ext{ first}, Win ext{ second})$ $= 0.18 + 0.18 = 0.36$

Thus, the probability that Sally wins exactly one of the two games against Martin is 0.36.