Question

On a particular day in July, there is a 20% probability of rain in Vancouver, a 65% probability of rain in Calgary, and a 75% probability of rain in Saskatoon. What is the probability that it will rain in all 3 cities on that day?

Answer 1

The probability that it will rain in all 3 cities on that day

P(V∪ C∪S) = 0.93 = 93%

Explanation:

Let 'V' be the event of rain in Vancouver

Given that the probability of rain in Vancouver

P( V) = 20% = 0.20

P( V⁻) = 1- P( V) = 1 - 0.20 =0.80

Let 'C' be the event of rain in Calgary

Given that the probability of rain in Calgary

P( C) = 65% = 0.65

P( C⁻) = 1- P( C) = 1 - 0.65 =0.35

Let 'S' be the event of rain in Saskatoon

Given that the probability of rain in Saskatoon

P( S) = 75% = 0.75

P( S⁻) = 1- P( S) = 1 - 0.75 =0.25

First we will prove that the probability that it will not rain in all 3 cities on that day

P( V⁻ ∩ C⁻ ∩ S⁻ ) = P( V⁻) P( C⁻) P(S⁻)

= 0.80 × 0.35 × 0.25

= 0.07

The probability that it will rain in all 3 cities on that day

P(V∪ C∪S) = 1-(P( V⁻ ∩ C⁻ ∩ S⁻ )

= 1 - 0.07

= 0.93