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Quiz of the Month (December 2007)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

   1. 0.0204
   2. 0.2069
   3. 0.0343


Notes. 1. (1/7)*(1/7) = 0.02041 2. Prob. no members born on Friday = (6/7)6 = 0.39657 No. of ways of choosing one member = 6 So prob. exactly one member born on Friday = 6 * (1/7) * (6/7)5 = 0.39657 So required prob. = 1 - 0.39657 - 0.39657 = 0.20686 3. No. of ways of choosing four members = 6C4 = 15 So prob. that exactly four members born on Friday = 15 * (1/7)4 * (6/7)2 = 0.004590 Similarly prob. exactly five members born on Friday = 6 * (1/7)5 * (6/7) = 0.000306 And prob. all six members born on Friday = (1/7)6 = 0.000008 So prob. at least four born on Friday = 0.004590 + 0.000306 + 0.000008 = 0.004904 So prob. at least four born on any one day = 7 * 0.004904 = 0.034328

THIS MONTH'S QUIZ

Four tangents are drawn to a circle as shown.
Find the values of each of the angles a, b, c, and d.
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© Hector C. Parr (2007)

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