Question

Assume that we have two events, A and B , that are mutually exclusive. Assume further that we know P(A) = 0.2 and P(B) = 0.8 . If an amount is zero, enter "0 ". A. What is P(A intersect B)? B. What is P(A|B)? C. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate? D. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

Answer 1

a)P(A n B)=0 (As A and B are mutually exclusive)

b)P(A|B)=P(A n B)/P(B)=0/0.8 =0

c)

here for mututally exclusive events P(A n B)=0

while for independent events P(A n B)=P(A)*P(B)

for two events to be mututally exclusive and indepednent ;at least one or both of P(A) or P(B) should be equal to 0

which is not always true ; so this statement is false

d)

we can conclude that mutually exclusive and independent events are different untill at least one of the events is empty set.