Can someone please explain how to do this problem?
The probability that it will rain today is 65%, and the probability that it will rain tomorrow is 25%. The probability that it will rain both days is 35%. What is the probability that it will rain today or tomorrow?
To find the probability that it will rain today or tomorrow, you need to use the principle of probability union.
The probability of the union of two events (A or B) is calculated by adding the probabilities of each event and then subtracting the probability of their intersection.
In this case, let's denote:
A = It will rain today
B = It will rain tomorrow
The probability of A is 65% (0.65), the probability of B is 25% (0.25), and the probability of the intersection (A and B) is 35% (0.35).
To find the probability of A or B, follow these steps:
1. Add the probabilities of A and B:
P(A or B) = P(A) + P(B)
P(A or B) = 0.65 + 0.25
2. Subtract the probability of their intersection:
P(A or B) = 0.65 + 0.25 - 0.35
3. Calculate the result:
P(A or B) = 0.9 - 0.35
P(A or B) = 0.55
Therefore, the probability that it will rain today or tomorrow is 55%.