If P(A) = .3 and P(B) = .4 and P(AandB) = .2
what is
P(A/B)? P(B/A)? Are A and B indepentent?
To find the conditional probability P(A/B) and P(B/A), we can use the formula:
P(A/B) = P(A ∩ B) / P(B)
P(B/A) = P(A ∩ B) / P(A)
Given: P(A) = 0.3, P(B) = 0.4, and P(A∩B) = 0.2, we can substitute these values into the formula:
P(A/B) = 0.2 / 0.4 = 0.5
P(B/A) = 0.2 / 0.3 ≈ 0.67
Now, to determine whether A and B are independent, we can compare the joint probability P(A ∩ B) with the product of the individual probabilities P(A) and P(B).
If P(A ∩ B) = P(A) * P(B), then A and B are independent.
In this case, P(A ∩ B) = 0.2, P(A) = 0.3, and P(B) = 0.4.
Let's check if P(A ∩ B) = P(A) * P(B):
0.2 ≠ 0.3 * 0.4
Since the equation doesn't hold true, A and B are not independent.