Homework #4 below. Suppose a The distribution of blood-Types and Rh-factors for

Question

Homework #4 below. Suppose a The distribution of blood-Types and Rh-factors for a population are given person is selected at random from this population. 1. Blood Type AB Positive0.380.34 0.09 0.03 tive 0.07 0.0 0.020.01 a. What is the probability that the person has type O blood? b. What is the probability that the person does not have type O blood? c. What is the probability that the person has Rh-negative blood? d What is the probability that the person has type O blood and is Rh-negative? e. What is the probability that the person has type O blood or is Rh-negative? f If the person has type O blood, what is the probability the person is Rh-negative? g. Are the events "Type O blood" and "Rh-negative mutually exclusive?" State "Yes" or h. Are the events "type O blood" and "Rh-negative independent?" State "Yes" or "No and i. Are the events "type O blood" and "type A blood" mutually exclusive? State "Yes" or No" and justify your answer mathematically justify your answer mathematically. "No" and justify your answer mathematically.

Explanation / Answer

(a) Probability that person has type O BG = 0.38 + 0.07 = 0.45

(b) Probability that person does not have type O BG = 1 - 0.45 = 0.55

(c) Probability that person has Rh-negative blood = 0.07 + 0.06 + 0.02 + 0.01 = 0.16

(d) Probability that person has type O and Rh-negative blood = 0.07

(e) Probability that person has type O or Rh-negative blood group = P(type O) + P(Rh-ve) - P(type O and Rh-ve) = 0.45 + 0.16 - 0.07 = 0.54

(f) Probability that the person is Rh-ve given that person has O blood group = P(Rh-ve | type O) = P(type O and Rh-ve)/ P(type O) = 0.07/0.45 = 0.1556

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