Conditional probability question

**msokol89** · November 25th 2011, 12:27 PM

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?

**mr fantastic** · November 25th 2011, 08:45 PM

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?

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

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

**msokol89** · November 25th 2011, 10:24 PM

Originally Posted by mr fantastic

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

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)

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