Given that P(A) = 0.6, P(B) = 0 .15, and P(A OR B) = 0.7, what is P(A AND B)?
Question
Given that P(A) = 0.6, P(B) = 0 .15, and P(A OR B) = 0.7, what is P(A AND B)?
Solution 1
To find the probability of A and B (P(A AND B)), we can use the formula for the union of two events:
P(A OR B) = P(A) + P(B) - P(A AND B)
We can rearrange this formula to solve for P(A AND B):
P(A AND B) = P(A) + P(B) - P(A OR B)
Substituting the given values into the formula:
P(A AND B) = 0.6 + 0.15 - 0.7
P(A AND B) = 0.05
So, the probability of both A and B occurring is 0.05.
Solution 2
To find the probability of A and B (P(A AND B)), we can use the formula for the union of two events:
P(A OR B) = P(A) + P(B) - P(A AND B)
We can rearrange this formula to solve for P(A AND B):
P(A AND B) = P(A) + P(B) - P(A OR B)
Substituting the given values into the formula:
P(A AND B) = 0.6 + 0.15 - 0.7
P(A AND B) = 0.05
So, the probability of both A and B occurring is 0.05.
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