Consider the archery competition in Example 6. Assume that Nina’s probability of hitting the bull’s-eye on a turn is 0.45 and that Brook’s probability is p. Assume that Nina goes first. For what value of p do both players have a probability of 1/2 of winning the competition?

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EXAMPLE 6 A Probability Computation Nina and Brook are participating in an archery competition where they take turns shooting at a target. The first one to hit the bullseye wins. Nina's success rate hitting the bullseye is 45%, while Brook's is 52%. Nina pointed out this difference, arguing that she should go first. Brook agreed to give the first turn to Nina. Should he have?