Question

BAYES FORMULA

9) At a retail store, 20% of customers use the store’s online app to assist them when shopping in the store ; 80% of store shoppers don’t use the app. Of those customers that use the online app while in the store, 50% are very satisfied with their purchases, 40% are moderately satisfied, and 10% are dissatisfied.

Of those customers that do not use the online app while in the store, 30% are very satisfied with their purchases, 50% are moderately satisfied and 20% are dissatisfied. Indicate the events by the following:

A = shopper uses the app in the store

N = shopper does not use the app in the store

V = very satisfied with purchase

M = moderately satisfied

D = dissatisfied

a. Find P(A and D), the probability that a store customer uses the app and is dissatisfied

b. Find P(A|D), the probability that a store customer uses the app if the customer is dissatisfied.

Answer 1

P(A) = 0.2

P(N) = 0.8

a) P(A and D) = P(D | A) * P(A)

                       = 0.1 * 0.2 = 0.02

b) P(A | D) = (A and D )/P(D)

                 = 0.02/(0.1 * 0.2 + 0.2 * 0.8)

                 = 0.1111