2008 2 - Stat 230 Spring 2008 STAT 230 - Spring 2008 - Test...

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Stat 230 Spring 2008 STAT 230 - Spring 2008 - Test 2 SOLUTIONS 1. [12 marks] Each person has either O, A, B, or AB type blood. O can receive donations from O only, A can receive from O or A, B can receive from O or B, and AB can receive from any type of blood. In Canada, the breakdown of population by blood type is as follows: O - 0 . 46 A - 0 . 42 B - 0 . 09 AB - 0 . 03 The probability a person with a given blood type will actually donate blood is as follows: O - 0 . 10 A - 0 . 07 B - 0 . 04 AB - 0 . 03 (a) [3 marks] What is the probability of a blood donation occuring? P ( D ) = P ( OD ) + P ( AD ) + P ( BD ) + P ( ABD ) = P ( D | O ) P ( O ) + P ( D | A ) P ( A ) + P ( D | B ) P ( B ) + P ( D | AB ) P ( AB ) = 0 . 10 * 0 . 46 + 0 . 07 * 0 . 42 + 0 . 04 * 0 . 09 + 0 . 03 * 0 . 03 = 0 . 0799 (b) [4 marks] Given a donation has occured, what is the probability a type B person can receive it? P ( O or B | D ) = P ( O | D ) + P ( B | D ) = P ( OD )+ P ( BD ) P ( D ) = P ( D | O ) P ( O )+ P ( D | B ) P ( B ) P ( D ) = 0 . 10 * 0 .
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2008 2 - Stat 230 Spring 2008 STAT 230 - Spring 2008 - Test...

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