Q5.The probability that it will rain today is 0.5, the probability that it will rain tomorrow is 0.6.The probability that it will rain either today or tomorrow is 0.7.What is the probability that it willrain today and tomorrow?
Question
Q5.The probability that it will rain today is 0.5, the probability that it will rain tomorrow is 0.6.The probability that it will rain either today or tomorrow is 0.7.What is the probability that it willrain today and tomorrow?
Solution
The problem can be solved using the formula of the probability of the union of two events, which is P(A U B) = P(A) + P(B) - P(A ∩ B). Here, A is the event that it will rain today, B is the event that it will rain tomorrow, and A ∩ B is the event that it will rain both today and tomorrow.
Given in the problem, we have:
P(A) = P(rain today) = 0.5 P(B) = P(rain tomorrow) = 0.6 P(A U B) = P(rain today or tomorrow) = 0.7
We need to find P(A ∩ B) = P(rain today and tomorrow).
Substituting the given values into the formula, we get:
0.7 = 0.5 + 0.6 - P(A ∩ B)
Solving for P(A ∩ B), we get:
P(A ∩ B) = 0.5 + 0.6 - 0.7 = 0.4
So, the probability that it will rain both today and tomorrow is 0.4.
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