Question

Q2. Chroma, a brick & mortar electronic store, recently conducted a study on its customers. It analysed that the probability of a customer entering the store during its discount sale and buying a refrigerator or a TV set is 0.32. If the probability of a customer to buy a refrigerator is 0.21 and that of buying a TV set is 0.16, what is the probability that the customer will buy both, refrigerator & the TV set? Also comment if the events of buying the refrigerator and the TV set independent.

Answer 1

probability of a customer entering the store during its discount sale and buying a refrigerator or a TV set is 0.32.

And

probability of a customer to buy a refrigerator is 0.21

and that of buying a TV set is 0.16,

Thus

P(Refrigerator)=0.21

P(TV set)= 0.16

P(Refrigerator or TV set )= 0.32

Now,

Probability that the customer will buy both refrigertor and The TV set is

P(Refrigerator and TV set)= P(Refrigerator )+ P(TV set) - P(Refrigerator or TV set)

= 0.21+0.16-0.32

= 0.05

Thus the probability that the customer will buy both, refrigerator & the TV set is 0.05

Now,

Two event A and B are indepedent if

P(A and B)= P(A).P(B)

Here

P(Refrigerator).P(TV set)= 0.21*0.16= 0.0336

Which is not equal to P(Refrigerator and TV set)= 0.05

Thus

P(Refrigerator and TV set) P(Refrigerator)* P(TV set)

Therefore

The events of buying the refrigerator and the TV set are not independent.