Suppose that we have two events, A and B, with P (A) = 0.40, P (B) = 0.60, and P (A ∩ B) = 0.20. (a) Find P (A | B). (Round your answer to four decimal places.) P (A | B) = (b) Find P (B | A). P (B | A) = (c) Are A and B independent? Why or why not? A and B independent because.

a.) 0.3333

b.) 0.5

c.) A and B are NOT independent

Step-by-step explanation:

We're given P (A) = 0.4, P (B) = 0.6, P (AnB)

a.) From law of probability,

P (A l B) = P (AnB) / P (B)

P (A l B) = 0.2/0.6 = 0.3333

b.) similarly, going by the above law of probability,

P (B l A) = P (BnA) / P (A)

P (B l A) = 0.2/0.4 = 0.5

c.) Two events A and B are said to be independent if mathematically, any of the following conditions are satisfied.

i.) P (A l B) = P (A)

ii.) P (B l A) = P (B)

Since both conditions stated above are not satisfied, that is:

P (A l B) [0.3333] ≠ P (A) [0.4]

P (B l A) [0.5] ≠ P (B) [0.6]

then the two events A and B are NOT Independent