Question

4.2.16 Use the contingency table below to find the following probabilities a. AlB d. Are events A and B independent? b. A/B c. AB. В' 40 20 30

Answer 1

a)

b)

$P(A|B') =\frac{P(A\cap B')}{P(B')} = \frac{20}{50} =0.4$

c)

$P(A'|B') =\frac{P(A'\cap B')}{P(B')} = \frac{30}{50} =0.6$

d)

P(A) = 60/110 = 6/11

P(B) = 60/110 = 6/11

P(A)*P(B) = (6/11)*(6/11) = 36/121

$P(A\cap B) =\frac{40}{110} = \frac{4}{11}$

$P(A\cap B) \neq P(A)P(B)$

Hence A and B re not independent.