With reference to the used car example and the probabilities given in Figure 3.9, find (a) (Pleft(M_{1} mid P_{1} ight)) and compare its value with

With reference to the used car example and the probabilities given in Figure 3.9, find

(a) \(P\left(M_{1} \mid P_{1}\right)\) and compare its value with that of \(P\left(M_{1}\right)\)

(b) \(P\left(C_{3} \mid P_{2}\right)\) and compare its value with that of \(P\left(C_{3}\right)\);

(c) \(P\left(M_{1} \mid P_{1} \cap C_{3}\right)\) and compare its value with that of \(P\left(M_{1}\right)\).

Data From Figure 3.9

Probability C 0.03 P C 0.06 M Pz P 5555555 0.07 0.02 0.01 0.01 0.09 C 0.16 0.10 M C 0.02 P2 C 0.07 C3 0.06 C 0.05 P C 0.05 C3 0.14 C 0.01 M3 P2 C 0.03 C3 0.02