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Suppose there are Uraguchi and non-Uraguchi(irregular) enrollees in the DoTeihen medical school.

they get the achievement test for high school students.

The failing rate of Uraguchi is known to distribute in β distributuion with its mode

The failing rate of irregulars is in β distribution with ω = 0.25 and κ = 12.

They correspond to Uraguchi ~ beta(8.5,3.5) and Irreglar ~ beta(3.5,8.5),respectively.

At a DoTeihen medical school, 9 alimni had the test, and 9 failed and 0 passed.

Infer the proportion of Uraguchi in this DoTeihen.

The graph shows their distribution.

http://i.imgur.com/h4TxJXQ.png