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Quiz of the Month (November 2004)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

    1.   8.5 cm, 7.5 cm, 10.5 cm.
    2.   14 cm, 17 cm, 19 cm, 21 cm, 22 cm.
    3.   2.1 cm.
Notes
 1. Suppose radii of circles with centres A, B, C are
       a, b, c cm respectively.
    So a + b     = 16
           b + c = 18
       a     + c = 19
    Solving, a = 8.5, b = 7.5, c = 10.5

 2. Solved similarly.

 3. It is easily seen that IJ + KL + MN = JK + LM + NI.
     So NI = IJ - JK + KL - LM + MN = 2.1

THIS MONTH'S QUIZ

A family consists of five children. If you know nothing to the contrary you may assume each is equally likely to be a boy or a girl.

1. What is the probability that the number of boys is three?

2. If you know there is at least one boy, what is the probability that the total number of boys is three?

3. If you know that the youngest child is a boy, what is the probability that the total number of boys is three?

***

© Hector C. Parr (2004)

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