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?

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

P (V∪ C∪S) = 0.93 = 93%

Step-by-step 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