Question

In: Statistics and Probability

Let A and B be two events in a sample space S. If P(A1Bc) =.10, P(Ac1B)...

Let A and B be two events in a sample space S. If P(A1Bc) =.10, P(Ac1B) =.40 and P(Ac1Bc) =.10,

a. Illustrate the events A1Bc, Ac1B and Ac1Bc on a van Venn-diagram

b. Check for the independence of events A and B.

c. Find P(A1B*AUB).

Expert Solution

ANSWER:::

(OR) FOR BETTER UNDERSTANDING

a)

below are the events with their corresponding area shaded

b)

here P(AUB) =1-P(AcBc) =1-0.1 =0.90

P(AnB) = P(AUB)-P(AcB)-P(ABc) =0.9-0.1-0.4 =0.4

and P(A) =P(ABc)+P(AnB) =0.1+0.4 =0.5

P(B)=P(AcB)+P(AnB)= 0.40+0.4=0.80

as P(A)*P(B)=0.5*0.80=0.40 which is eqaul to P(AnB) therefore A and B are independent.

c)

P(AB|AUB) =P(AB & AUB)/P(AUB)=P(AB)/P(AUB) =0.4/0.90=4/9=0.4444

orchestra answered 2 years ago

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