Question

Amazon's third-largest market is the United Kingdom. In 2019, the employees at a local firm in London received their salary and decided to spend a portion of it on making online purchases from Amazon. The probability that the online purchases will be shipped on time to each employee is 0.68. Determine the following:

a. The probability that three products will be shipped on time.

b. The probability that out of three, two products will be shipped on time.

Answer 1

Solution :

Given that, the probability that the online purchases will be shipped on time to each employee is 0.68.

a) We have to obtain the probability that three products will be shipped on time.

Using multiplication theorem of probability we shall get the probability that three products will be shipped on time.

The probability that three products will be shipped on time = 0.68 × 0.68 × 0.68 = 0.314432.

b) We have to obtain the probability that out of thrre, two products will be shipped on time.

If out of three products, two product will be shipped on time, then one product will not be shipped on time.

Probability that a product will not be shipped on time will be (1 - 0.68) = 0.32.

And probability that two products will be shipped on time will be (0.68 × 0.68) = 0.4624

Total number of ways of selecting 2 product from 3 products which will be shipped on time is given by,

Hence, probability that out of three, two products will be shipped on time is,

The probability that out of three, two products will be shipped on time is 0.443904.