5.4 solutions

# A person with type b blood can receive a transfusion

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A person with type B blood can receive a transfusion from someone with type B or type O blood. What’s the chance of being able to receive a transfusion if you have type B blood? P(B or O) = P(B) + P(O) {because they are disjoint} = .11 + .45 = .56 b. Select two people at random. What is the chance they both have type B blood? P(B 1 and B 2 ) = P(B 1 ) x P(B 2 ) = (.11)(.11) = .0121 c. Select two people at random. What is the chance they both have the same blood type? P(both O) + P( both A) + P(both B) + P(both AB)

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Independent = P(O)P(O) + P(A)P(A) + P(B)P(B) + P(AB)P(AB) = (.45) 2 + (.40) 2 + (.11) 2 + (.04) 2 = .3762 d. Select two people at random. What is the chance that one has type A blood and the other has type B blood? P(A 1 and B 2 ) + P(B 1 and A 2 ) = P(A)P(B) + P(B)P(A) = (.40)(.11) + (.11)(.40) = .088 e. Select two people at random. What is the chance that exactly one has type A blood? P(A 1 and not A 2 ) + P(not A 1 and A 2 ) = P(A)P(not A) + P(not A)P(A) = (.4)(.6) + (.4)(.6) = .48 Problem 3 The following table lists the joint probabilities associated with having a fast car and the number of speeding tickets in the last 6 months. Suppose we select a car owner at random from this sample. Are owning a fast car and getting more than 1 speeding ticket independent? Use probabilities and show your work.
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