Let 𝐴 be the event that it rains on Monday and let 𝐵 be the event that it rains on Tuesday. Given that the probability of 𝐴 is 0.7 and the probability of 𝐵 is 0.5, find the probability that it rains on both days if the events are independent.
The keyword in this question is “independent”. We recall that if two events 𝐴 and 𝐵 are independent, then the probability of 𝐴 intersection 𝐵, both 𝐴 and 𝐵 occurring, is equal to the probability of 𝐴 multiplied by the probability of 𝐵. In this question, the probability that it rains on both days is equal to the probability it rains on Monday multiplied by the probability it rains on Tuesday. We need to multiply the probability of 𝐴 by the probability of 𝐵. We’re told that these are equal to 0.7 and 0.5, respectively. Multiplying these gives us 0.35.
The probability that it rains on both days is therefore equal to 0.35.