# Probability test question

• Feb 9th 2010, 12:05 PM
BrownianMan
Probability test question
I had this question on a test:

The probability of snowing in one city is 0.4, and the probability of snowing in another city is 0.7. Assume independence. What is the probability that it snows in exactly one of the two cities?

The way I approached it was to say that the probability that it snows in exactly one of the two cities is:

Let A denote probability of snow in the first city.
Let B denote probability of snow in the second city.

P(A and 'not B') or P('not A' and B) = (0.4)(0.3) + (0.6)(0.7) - (0.4)(0.3)(0.6)(0.7) = 0.4896

Is this correct?
• Feb 9th 2010, 12:11 PM
icemanfan
There are four possibilities:

It snows in neither city

P1 = (0.6)(0.3)

It snows in both cities

P2 = (0.4)(0.7)

It snows in the first city only

P3 = (0.4)(0.3)

It snows in the second city only

P4 = (0.6)(0.7)

The probability that it snows in exactly one city is simply P3 + P4.
• Feb 9th 2010, 12:15 PM
Plato
Quote:

Originally Posted by BrownianMan
The probability of snowing in one city is 0.4, and the probability of snowing in another city is 0.7. Assume independence. What is the probability that it snows in exactly one of the two cities?
Let A denote probability of snow in the first city.
Let B denote probability of snow in the second city.
P(A and 'not B') or P('not A' and B) = (0.4)(0.3) + (0.6)(0.7) - (0.4)(0.3)(0.6)(0.7) = 0.4896

Is this correct?

No the part in red is not correct.
Think about it. Can A and notA both happen?