Suppose that 40% of Australian cattle dogs have black coats; these individuals are commonly referredto as "Blue Heelers" as opposed to "Red Heelers". Among Blue Heelers, 35% of individualshave bilateral masks and 25% have unilateral masks. About 50% of Red Heelers exhibit no eyemasking and 10% have bilateral masks. Let M represent the event that an Australian cattle dog has a facial mask, where M2 represents abilateral mask, M1 represents a unilateral mask, and M0 indicates lack of a mask.
a) Calculate the probability an Australian cattle dog has a facial mask and a black coat. b) Calculate the prevalence of bilateral masks in Australian cattle dogs. c) Among Australian cattle dogs with bilateral facial masks, what is the probability ofbeing a Red Heeler?d) Unilateral deafness occurs in Red Heelers with probability 0.15, in both dogs thateither lack facial masking or exhibit a unilateral mask; for both unmasked and unilaterallymasked Red Heelers, 60% of dogs are not deaf. The overall prevalence of bilaterally masked