Conditional probability question

On a wintry day, a salesman randomly chooses to drive to 2 of the following three cities: Los Angeles, San Francisco, and Sacramento.

The probability of rain on a wintry day is:

1/3 in San Francisco

1/4 in Sacramento

1/6 in Los Angeles

He returned home with wet clothes.

What is the probability he had visited Los Angeles?

Re: Conditional probability question

Quote:

Originally Posted by

**msokol89** On a wintry day, a salesman randomly chooses to drive to 2 of the following three cities: Los Angeles, San Francisco, and Sacramento.

The probability of rain on a wintry day is:

1/3 in San Francisco

1/4 in Sacramento

1/6 in Los Angeles

He returned home with wet clothes.

What is the probability he had visited Los Angeles?

$\displaystyle \frac{\frac{1}{3} \times \frac{1}{6}}{\frac{1}{3} \times \frac{1}{6} + \frac{1}{3} \times \frac{1}{3} + \frac{1}{3} \times \frac{1}{4}} = .... $

Your job is to review conditional probability so that you understand where this expression has come from.

Re: Conditional probability question

Quote:

Originally Posted by

**mr fantastic** $\displaystyle \frac{\frac{1}{3} \times \frac{1}{6}}{\frac{1}{3} \times \frac{1}{6} + \frac{1}{3} \times \frac{1}{3} + \frac{1}{3} \times \frac{1}{4}} = .... $

Your job is to review conditional probability so that you understand where this expression has come from.

I understand where this expression has come from, however you have missed the part where it says the salesman visited 2 of the 3 cities.

Your answer is correct for the case the salesman has visited only 1 of the 3 cities (2/9).

The answer to my question should be 0.621.

My problem is that I don't how to reach it.

(Sorry for my English)