An article in the Harvard Business Review discusses new products and services offered by the famous British department store Marks & Spencer.3 Suppose that Marks & Spencer plans to offer a new line of women's shoes and estimates the proportion of its customers who will be interested in the new line using the following probability distribution:

Proportion ...Probability

0.3 ....... 0.1

0.4 ....... 0.3

0.5 ....... 0.3

0.6 ....... 0.2

0.7 .......0.05

0.8 .......0.05

A survey of 20 randomly selected customers reveals that 5 of them are interested in the new line. Compute the posterior probability distribution.