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(i) Anna is to play Ben at tennis and squash. The probability that Anna wins the tennis match is 0.8. The probability that Anna

 

(i) Anna is to play Ben at tennis and squash. The probability that Anna wins the tennis match is 0.8. The probability that Anna wins at squash is 0.4. What is the probability that Anna wins at least one of the two matches? (ii) What is the probability that Anna wins both matches? (iii) Anna tosses a coin three times and records the number X of heads. If X is odd then Anna pays Ben X2 euro. Otherwise, Ben pays Anna X2 euro. What is the expected value of Anna's winnings on this game?

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