A quality control engineer believes that the proportion of defective items in a production process is a random variable with a probability distribution that is approximated as follows:

x .........P(x)

0.1 ........0.1

0.2 ........0.3

0.3 ........0.2

0.4 ........0.2

0.5 ........0.1

0.6 ........0.1

The engineer collects a random sample of items and finds that 5 out of the 16 items in the sample are defective. Find the engineer’s posterior probability distribution of the proportion of defective items.