Three teams, the Bats, the Cats, and the Rats, are the only competitors in a tou

Question

Three teams, the Bats, the Cats, and the Rats, are the only competitors in a tournament which which will have one (and only one) winner. A fan proposes the following function as a probability function for the winner of the tournament: P(no one wins) = 0 P(Bats win) = 0.72; P(Cats win) = 0.50; P(Rats win) = -0.22; P(Bats or Cats win) = 1.22; P(Bats or Rats win) = 0.51; P(Cats or Rats win) = 0.28; P(Bats or Cats or Rats win) = 1.01. Identify some reasons that this is not a valid probability function. (Select all that apply.)

(1)There are no reasons; this is a valid probability function.

(2)P(Bats win), P(Cats win), and P(Rats win) are not all equal.

(3)The probability of the sample space is not equal to 1.

(4)The probability of the empty set is not equal to 0.

(5)P(Bats or Rats win) is not equal to P(Bats win) + P(Rats win).

(6)P(Cats win) is less than P(Bats win).

(7)P(Rats win) is negative.

(8)P(Bats or Cats win) is greater than 1.

(9)P(Cats or Rats win) is equal to P(Cats win) + P(Rats win).

Explanation / Answer

The reasons that this is not a valid probability function is:

(3)The probability of the sample space is not equal to 1.

8)P(Bats or Cats win) is greater than 1.

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