2. 0.509
3. 0.422
4. 0.9905=99.05%
5 a) 1 - p^2
b) 1 - 4p^3 + 3p^4
c) 1/3 < p < 1
6. 0.04539
7. 1.9% Professors are faulty.
Posterior probability that a Professor was made
in England given that it was found to be faulty is 0.4210,
i.e. 42.10%.