# Heavy Traffic Word Problem

#### ByoungSuh

You are rushing out to get to your appointment in 30 minutes. From experience you know that most of the time you travel this distance in 30 minutes. However, half of the time there is heavy traffic. In the past, there has been heavy traffic and you have made it to your appointment within 30 minutes 34% of the time.
You get out on the street and see that there is heavy traffic. What is the chance you will get to your appointment on time?

Why is the answer .68 rather than just .34? Can someone explain this to me? And what formula or principle do you use? Ty.

#### DenisB

Who is the demented teacher who made that up?

#### ByoungSuh

Lol Idk he's from the University of Amsterdam I forget his name. Why?

#### ByoungSuh

The answer is supposedly .68. I just don't know exactly why this is so and therefore it won't do me any good to know it's .68 for subsequent problems.

#### Debsta

MHF Helper
I think this is a really badly worded question.
If we let H mean "heavy traffic" and T mean "get there on time", then "half of the time there is heavy traffic" means that P(H)=0.5.

"In the past, there has been heavy traffic and you have made it to your appointment within 30 minutes 34% of the time." This is the wording of this question I don't like. To get the answer you say is correct, this has to be taken to mean P(H and T) = 0.34.

"You get out on the street and see that there is heavy traffic. What is the chance you will get to your appointment on time?"
So you are given that there is heavy traffic, so you need to find P(T l H).

So using P(T l H) = P(H and T) / P(T) you get 0.34/0.5 = 0.68.

As I said, the bit in the middle of the question is badly worded.

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