Gamblers usually give odds against an event happening. Forinstance, if a bookie gives the odds 4 to 1 that a certain team will win anevent, he is stating that the probability that the team will win is 15 or 0.2.Also, if a bettor bets$1 that the team will win and they dowin, then the bettor will receive$5 (his original bet plus a profit of$4).

Suppose a bookie has set the odds for the eventual winner in afour-team league. Use the information to answer the questions.

Team A (3 to 1), Team B (3 to 1), Team C (4 to 1), and Team D (4 to 3)

a) Convert the odds to probabilities of winning for each team

( write an integer or simplified fraction)

Pr(Team A)=

Pr(Team B)=

Pr(Team C)=

Pr(Team D)=

b) Add the four probabilities.

Pr(Team A)+Pr(Team B)+Pr(Team C)+Pr(Team D)=

c) Explain why the answer to b) makes sense. Choose the correct answer below.

A.The bookie makes the odds so that the sum of the probabilities are greater than 1 so that he can get more bets that will lose.

B.The bookie makes the odds so that the sum of the probabilities are greater than 1 so that he makes a profit whether the team wins or loses.

C.The bookie makes the odds so that the sum of the probabilities are greater than 1 because gambling regulations require it.

D.The bookie makes the odds so that the sum of the probabilities are greater than 1 so that the bettor thinks he has a better chance to win than he really does.