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Quiz of the Month (March 2005)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

   1.  48 ml.
   2.  30 mpg.
   3.  32.4 mpg.

Notes
  Suppose fuel used before start  = x gal.
  and fuel used for each 20 ml of journey = y gal.

  So distance travelled before start = 36x ml.
    So   (36x+20)/(x+y) = 34
    and (36x+40)/(x+2y) = 33

  Solving:  x = 1 1/3, y = 2/3

  So:   1. Distance = 36x = 48 ml
        2. mpg = 20/y = 30
        3. Reading = (36x+60)/(x+3y) = 32.4 mpg

THIS MONTH'S QUIZ

The sock-drawer in my bedroom contains 8 black socks, 6 grey ones and 2 brown ones. Just as I am about to select a pair, the light fails and the room is plunged into darkness.

1. If I pick out two socks at random, find the probability that they form a matching pair.

2. If I pick out three socks at random and take them into a lighted room, find the probability that they include a matching pair.

3. If I pick out four socks at random and take them into a lighted room, find the probability that they include at least one matching pair.

***

© Hector C. Parr (2005)

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