Question

Victor must choose one pair of pants, one shirt, and one tie to wear to work. his possible choice combinations are shown on the tree diagram below.if victor chooses these work clothes at random, what is the probability that he will choose tan pants, a white shirt, and a red tie?

Answer 1

Given: Victor must choose one pair of the pants, shirt, and tie to wear to work.

Required: To find out if Victor chooses these work clothes randomly, what is the probability that he will choose tan pants, a white shirt, and a red tie.

Explanation: Since Victor has two choices for Pants, Tan or Black.

Hence

`P(Pant)=(1)/(2)`

Now, For the Shirt, he has three choices,

`P(Shirt)=(1)/(3)`

He has two ties, which are red and blue, so the probability of choosing the red tie is

`P(Tie)=(1)/(2)`

Hence the required probability is

`\begin{gathered} P=P(Pant)* P(Shirt)* P(Tie) \\ =(1)/(2)*(1)/(3)*(1)/(2) \\ =(1)/(12) \end{gathered}`

Final Answer: The required probability of the event is

`P=(1)/(12)`