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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 = ^{6}C_{4} = 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.

 

***
© Hector C. Parr (2007)
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