Suppose the probability that it rains today is 40%, the probability it rains tomorrow is 50%, and the probability it rains tomorrow given that it rains today is 25%. Find the probability that it rains both today and tomorrow.
To find the probability that it rains both today and tomorrow, we can use the concept of conditional probability.
Let's denote the event that it rains today as "A" and the event that it rains tomorrow as "B". We are given the following probabilities:
P(A) = 0.40 (probability that it rains today)
P(B) = 0.50 (probability that it rains tomorrow)
P(B|A) = 0.25 (probability that it rains tomorrow given that it rains today)
We can use these probabilities to calculate the probability of both events happening simultaneously, denoted as P(A ∩ B) or P(A and B).
We can use the formula for conditional probability:
P(A ∩ B) = P(A) * P(B|A)
Substituting the given values:
P(A ∩ B) = 0.40 * 0.25 = 0.10
Therefore, the probability that it rains both today and tomorrow is 0.10 or 10%.