OCR MEI S1 — Question 3

Exam BoardOCR MEI
ModuleS1 (Statistics 1)
TopicProbability Definitions
TypeListing outcomes and counting

3 Sophie and James are having a tennis competition. The winner of the competition is the first to win 2 matches in a row. If the competition has not been decided after 5 matches, then the player who has won more matches is declared the winner of the competition. For example, the following sequences are two ways in which Sophie could win the competition. ( \(\mathbf { S }\) represents a match won by Sophie; \(\mathbf { J }\) represents a match won by James.) \section*{SJSS SJSJS}
  1. Explain why the sequence \(\mathbf { S S J }\) is not possible.
  2. Write down the other three possible sequences in which Sophie wins the competition.
  3. The probability that Sophie wins a match is 0.7 . Find the probability that she wins the competition in no more than 4 matches.