January 2008 - Question 5



This is an easy mark to pick up if you read the question.
As the question says, "The winner of the competition is the first to win 2 matches in a row," where SSJ shows that Sophie has already won two matches and therefore won the competition so the further match where James won would not occur.




This is an easy question again, you just need to make sure that the S occurs twice before J occurs twice.
SS, JSJSS, JSS.




As we worked out earlier, there are 4 different ways Sophie can win the competition. But as we need to find out the probability that she wins no more than 4 games, we'll have to rule out this one - JSJSS.
If she won the competition, she'd have to get two 0.7s in a row, so we can call this 0.72.
We can call James winning 0.3.
So the different ways she could win:

SS = 0.72 = 0.49
JSS = 0.3 × 0.72 = 0.147
SJSS = 0.7 × 0.3 × 0.72 = 0.1029


Now we just need to add these together.

0.49 + 0.147 + 0.1029 = 0.7399

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