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# 11_28_11_2ans - STAT 409 1 Fall 2011 Examples for(2 A...

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STAT 409 Examples for 11/28/2011 (2) Fall 2011 1. A statistics instructor teaches two statistics classes, one in the morning and one in the afternoon. Suppose the probability that the instructor gives a good morning lecture is 0.3. If the morning lecture is good, then the afternoon lecture is also good with probability 0.70. However, if the morning lecture is bad, then there is an 80% chance that the afternoon lecture will also be bad. M = {good morning lecture}, A = {good afternoon lecture}. P( M ) = 0.30 (the probability that the instructor gives a good morning lecture is 0.3) P( A | M ) = 0.70 (if the morning lecture is good, then the afternoon lecture is also good with probability 0.70) P( A ' | M ' ) = 0.80 (if the morning lecture is bad, then there is an 80% chance that the afternoon lecture will also be bad) a) What proportion of the afternoon lectures are bad? P( A ' ) = P( M A ' ) + P( M ' A ' ) = P( M ) P( A ' | M ) + P( M ' ) P( A ' | M ' ) = 0.30 0.30 + 0.70 0.80 = 0.09 + 0.56 = 0.65 . OR P( A ' ) = 0.09 + 0.56 = 0.65 . OR

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A A ' Total M 0.30 0.70 0.21 0.09 0.30 M ' 0.14 0.70 0.80 0.56 0.70 Total 0.35 0.65 1.00 b) Suppose the afternoon lecture was good.
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