Question: You are evaluating the player selection process used by a major league baseball team. The team gives a bonus to 10% of the players that

You are evaluating the player selection process used by a major league baseball team. The team gives a bonus to 10% of the players that it signs to a contract, 30% of the players who were obtained through a trade, and the remainder did not receive a bonus. Examination of the player records for the past five years indicates that 40% of the players who were on the major league roster for at least one year received an initial signing bonus. In addition, 30% of the players on the major league roster for at least one year did not receive an initial signing bonus. The remaining players were obtained from trades. For those players who were signed and did not make the major league roster, 20% had received bonuses and 70% had not, with the remainder coming from trades. Of all players signed or obtained in trades, 20% are on the major league roster for at least one year.
a. What is the probability that a player who received a bonus is on the major league roster for at least one year?
b. What is the probability that a player who did not receive a bonus is on the major league roster for at least one year?
c. Should a player insist on a signing bonus because this will increase his probability of being on the major league roster?

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