Question

Use the contingency table below to find the following probabilities a. AB b. AB' C. A'B' d. Are events A and B independent? a. P(A/B) (Round to two decimal places as needed.) b. P(AIB') = c. P(A'B') = (Round to two decimal places as needed.) (Round to two decimal places as needed.) d. Are events A and B independent? O O A and B are not independent. A and B are independent.

Answer 1

Solution:

Given:

	B	B'	Total
A	40	20	60
A'	20	50	70
Total	60	70	N= 130

Part a) Find:

P(A | B) = .............?

P(A | B) = n( A and B) / n(B)

where n(A and B) = Number of outcomes of A and B = 40 and n(B) = total outcomes of B = 60

P(A | B) = 40 / 60

P(A | B) = 0.67

Part b) Find:

P(A | B') = .............?

P(A | B') = n( A and B') / n(B')

where n(A and B') = Number of outcomes of A and B' = 20 and n(B') = total outcomes of B = 70

P(A | B') = 20 / 70

P(A | B') = 0.29

Part c) Find:

P(A' | B') = .............?

P(A' | B') = n( A' and B') / n(B')

where n(A' and B') = Number of outcomes of A' and B' = 50 and n(B') = total outcomes of B = 70

P(A' | B') = 50 / 70

P(A' | B') = 0.71

Part d) Are events A and B independent?

P(A | B) = 0.67

P(A) = n(A) / N

P(A) = 60/130

P(A) = 0.46

Since P(A | B) $\neq$ P(A) , A and B are not independent events.