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Example Class 2 (sln)

Example Class 2 (sln) - The University of Hong Kong...

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The University of Hong Kong Department of Statistics and Actuarial Sciences STAT1801 Probability and Statistics: Foundations of Actuarial Sciences (10-11) Example Class 2 1. Urn 1 contains four red, three blue and two green balls while Urn 2 contains two red, three blue, and four green balls. A ball is drawn from urn 1 and put into urn 2. The balls in Urn 2 are then mixed, and one is drawn at random. (a) What is the probability that both balls drawn are red in color? 𝑃𝑃 ( 𝑏𝑏𝑏𝑏𝑏𝑏ℎ 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑏𝑏𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑟𝑟 ) = 𝑃𝑃 (2 𝑛𝑛𝑟𝑟 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑎𝑎𝑎𝑎𝑟𝑟 1 𝑏𝑏𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑎𝑎𝑎𝑎𝑟𝑟 ) = 𝑃𝑃 (2 𝑛𝑛𝑟𝑟 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑎𝑎𝑎𝑎𝑟𝑟 |1 𝑏𝑏𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑎𝑎𝑎𝑎𝑟𝑟 ) 𝑃𝑃 (1 𝑏𝑏𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑎𝑎𝑎𝑎𝑟𝑟 ) = 3 10 × 4 9 = 2 15 (b) What is the probability that a blue ball is drawn from Urn 2? 𝑃𝑃 (2 𝑛𝑛𝑟𝑟 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑎𝑎 ) = 𝑃𝑃 (2 𝑛𝑛𝑟𝑟 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑎𝑎 1 𝑏𝑏𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑎𝑎 ) + 𝑃𝑃 (2 𝑛𝑛𝑟𝑟 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑎𝑎 1 𝑏𝑏𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑛𝑛𝑏𝑏𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑎𝑎 ) = 𝑃𝑃 (2 𝑛𝑛𝑟𝑟 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑖𝑖𝑏𝑏 𝑏𝑏𝑏𝑏𝑏𝑏𝑎𝑎 |1 𝑏𝑏𝑏𝑏
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