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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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