Probability

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sanjuea
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People have one of four different blood types – O, A, B or AB. Suppose 50% of the population have blood type O, 37% have type A, 10% have type B and 3% have type AB.a) What is the probability that a randomly selected person’s blood type is:i) not type B?ii) is type A or type O?iii) is neither type O nor type B?b) Among 4 random people, what is the probability thati) all have type A?ii) none of them are type B?iii) at least one person is type O?iv) the second person is the only person with type O blood?
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lionpunkgirl
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(Original post by sanjuea)
People have one of four different blood types – O, A, B or AB. Suppose 50% of the population have blood type O, 37% have type A, 10% have type B and 3% have type AB.a) What is the probability that a randomly selected person’s blood type is:i) not type B?ii) is type A or type O?iii) is neither type O nor type B?b) Among 4 random people, what is the probability thati) all have type A?ii) none of them are type B?iii) at least one person is type O?iv) the second person is the only person with type O blood?
Note: O:0.5, A:0.37, B:0.1, AB:0.03


A)
i) P of not type B= 1-0.1=0.9
ii) Type A or O= 0.5+0.37=0.87
iii) Not type O or B= 1-0.5-0.1=0.4

B)
i) P that all 4 have type A= 0.37x0.37x0.37x0.37= (0.37)^4
ii) none of them have type B= (P of not type B)^4= (0.9)^4
iii) At least one is type O= 1- none have type O= 1- (1-0.5)^4= 1- (0.5)^4
iv) second person only person with type o blood= (not have type O) x (have type O) x (not have type O) x (not have type O)
= (1-0.5) x 0.5 x (1-0.5) x (1-0.5)
= (0.5)^4
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