Question

Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% are shipped to the people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other people, but for only 10% of the orders shipped to the person making the order.
a. What is the probability that a randomly selected order will be a gift wrapped and sent to a person other than the person making the order?
b. What is the probability that a randomly selected order will be gift wrapped?
c. Is gift wrapping independent of the destination of the gifts? Justify your response statistically?

Answer 1

Answer:

0.18 ; 0.1875 ; No

Step-by-step explanation:

Let:

Person making the order = P

Other person = O

Gift wrapping = w

P(p) = 0.7 ; P(O) = 0.3 ; p(w|O) = 0.60 ; P(w|P) = 0.10

What is the probability that a randomly selected order will be a gift wrapped and sent to a person other than the person making the order?

Using the relation :

P(W|O) = P(WnO) / P(O)

P(WnO) = P(W|O) * P(O)

P(WnO) = 0.60 * 0.3 = 0.18

b. What is the probability that a randomly selected order will be gift wrapped?

P(W) = P(W|O) * P(O) + P(W|P) * P(P)

P(W) = (0.60 * 0.3) + (0.1 * 0.7)

P(W) = 0.18 + 0.07

P(W) = 0.1875

c. Is gift wrapping independent of the destination of the gifts? Justify your response statistically

No.

For independent events the occurrence of A does not impact the occurrence if the other.