[The following information applies to the questions displayed below.] Four women

Question

[The following information applies to the questions displayed below.]

Four women’s college basketball teams are participating in a single-elimination holiday basketball tournament. If one team is favored in its semifinal match by odds of 1.40 to 1.60 and another squad is favored in its contest by odds of 2.30 to 1.70, what is the probability that:

A.

Both favored teams win their games? (Round your answer to 4 decimal places.)

Probability:

B.

Neither favored team wins its game? (Round your answer to 4 decimal places.)

Probability:

C.

At least one of the favored teams wins its game? (Round your answer to 4 decimal places.)

Probability:

Four women’s college basketball teams are participating in a single-elimination holiday basketball tournament. If one team is favored in its semifinal match by odds of 1.40 to 1.60 and another squad is favored in its contest by odds of 2.30 to 1.70, what is the probability that:

A.

Both favored teams win their games? (Round your answer to 4 decimal places.)

Probability:

B.

Neither favored team wins its game? (Round your answer to 4 decimal places.)

Probability:

C.

At least one of the favored teams wins its game? (Round your answer to 4 decimal places.)

Probability:

Explanation / Answer

Four women’s college basketball teams are participating in a single-elimination holiday basketball tournament. If one team is favored in its semifinal match by odds of 1.40 to 1.60

P(WIN)=1.40/3  

P(LOSE)=1.60/3

and another squad is favored in its contest by odds of 2.30 to 1.70

P(WIN)=2.30/4

P(LOSE)=1.70/4

(a) Both favored teams win their games?

       P(both wins) = (1.40/3)(2.30/4)

                            = 3.22/12

                            =0.2683

(b) Neither favored team wins its game?

      P(both lose) = (1.60/3)(1.70/4)

                          = 2.72/12

                          = 0.2266

(c) At least one of the favored teams wins its game?

          P(At least one wins) = 1-P(both lose)

                                          = 1-2.72/12

                                      =0.7733

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