Question

Casey is going to wear a gray sportcoat and is trying to decide what tie he should wear towork. In his closet, he has 26 ties, 20 of which he feels go well with the sportcoat. If Caseyselects one tie at random, determine the probablity and the odds of the tie going well or notgoing well with the sportcoat.The probability the tie goes well with the jacket is(Simplify your answer. Type an integer or a fraction.)Enter your answer in the answer box and then click Check Answer.Clear AllCheck Answerpartsremaining

Answer 1

The total ties=26

The number of ties go well with the sportcoat =20

It implies the number of ties that doesn't go well with the sportcoat=26-20=6

A tie is selected at random ,

The probability that it goes well with the sportcoat is,

$\begin{gathered} P=\frac{Desired\text{ outcomes}}{\text{total outcomes}} \\ P=\frac{20}{26} \\ P=\frac{10}{13} \end{gathered}$

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

$\begin{gathered} P=\frac{Desired\text{ outcomes}}{\text{total outcomes}} \\ P=\frac{6}{26} \\ P=\frac{3}{13} \end{gathered}$

The odds is given by,

$\begin{gathered} \text{Odds =}\frac{\text{ways you want}}{\text{ways you dont want}} \\ =\frac{20}{6} \\ =\frac{10}{3} \end{gathered}$

Answer:

1) The odds of of the tie going well or not going well with the sportcoat is 10/3

2) The probability that tie goes well with the jacket is 10/13.

3) The probability that tie will not go well with the jacket is 3/13.