Question

A given phenomenon has three events A,B, and C whose probabilities are given as 0.32, 0.23, and 0.11 respectively

a. What are the values of P(A and B), P(B and C), and P(C and A) if all three events A, B, and C are mutually exclusive

b. What are the values of P(A and B), P(B and C), and P(C and A) if all three events A, B, and C are independent of one another

c. What are the values of P(A and B), P(B and C), and P(C and A) if all three events A, B, and C are neither independent nor mutually exclusive

e. What is the value of P(A or B) if A and B are neither mutually exclusive nor independent

Answer 1

a)

if two events are mutually exclusive, then probability of their intersection is zero.

P(A and B) = 0

P(B and C) = 0

P(C and A) =0

b)

if two events rae independent then

P( A and B) = P(A)*P(B) = 0.32*0.23=0.0736

P(B and C) = P(B)P(C) = 0.23*0.11=0.0253

P(C and A) = P(C)P(A) = 0.32*0.11=0.0352

c)

if all three events A, B, and C are neither independent nor mutually exclusive, then their probability cannot be determined from given information

d)

since, A and B are neither mutually exclusive nor independent so, P( A and B) cannot be determined from given information

hence, P(A or B) cannor be calculated