Question

Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his​ closet, he has 22 ​ties, 13 of which he feels go well with the sportscoat. If Casey selects one tie at​ random, determine the probability and the odds of the tie going well or not going well with the sportscoat.

The probability the tie goes well with the jacket is?

The probability the tie will not go well with the jacket is?

The odds against the tie going well with the jacket is?

(Simplify your answer. Type an integer or a​ fraction.)

The odds in favor of the tie going well with the jacket is? ​

(Simplify your answer. Type a ratio using a​ colon.)

Answer 1

The probability that the tie goes well with the jacket is:

P(going well) = number of ties that go well / total number of ties
P(going well) = 13/22
P(going well) = 0.59 or 59%

The probability that the tie will not go well with the jacket is:

P(not going well) = 1 - P(going well)
P(not going well) = 1 - 0.59
P(not going well) = 0.41 or 41%

The odds against the tie going well with the jacket is:

Odds against = number of ties that do not go well / number of ties that go well
Odds against = (22-13) / 13
Odds against = 9/13

The odds in favor of the tie going well with the jacket is:

Odds in favor = number of ties that go well / number of ties that do not go well
Odds in favor = 13 / (22-13)
Odds in favor = 13/9 or 1.44:1

(If this doesn’t seem right to you comment!)