A firm is contemplating the purchase of 500 printer cartridges. One supplier, supplier A, offersthe cartridges at $15 each, guarantees each cartridge, and will replace all defective cartridgesfree. A second supplier, supplier B, offers the cartridges at $14 each with no guarantee.However, supplier B will replace defective cartridges with good cartridges for $10 per cartridge.Suppose that the proportion of defective cartridges produced by supplier B is denoted by ~p, andsuppose that the prior distribution for ~p is a beta distribution with parameters r'= 2 and n'= 50.(a) (5 points) What should the firm do on the basis of the prior distribution?(b) (10 points) In the sample of 10 cartridges, 1 is defective. Find the posterior distribution of ~pand use this distribution to determine which supplier the firm should deal with