American Airlines is interested in the proportion of flights that are full during the 2008 summer season. The airline uses data from past experience and constructs the following prior distribution of the proportion of flights that are full to capacity:

S .....P(S)

0.70 ....0.1

0.75 .....0.2

0.80 .....0.3

0.85 .....0.2

0.90 .....0.1

0.95 .....0.1

1.0

A sample of 20 flights shows that 17 of these flights are full. Update the probability distribution to obtain a posterior distribution for the proportion of full flights.