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WAEC 2011 · Paper 2 · Q6

  1. (a)

    In a physics examination, the mean mark of the first twelve students in a class is 60, that of the next twenty students is 50 and that of the remaining yy students is xx. What is the mean mark for the whole class, in terms of xx and yy?

  2. (b)

    A box contains 4 red and 3 blue identical balls. If two balls are picked at random, one after the other without replacement, find the probability that one is red and the other blue.

Worked solution (try it first)

(a)

  1. Total marks: 12×60+20×50+xy=720+1000+xy12 \times 60 + 20 \times 50 + xy = 720 + 1000 + xy
    =1720+xy= 1720 + xy.
  2. Number of students: 12+20+y=32+y12 + 20 + y = 32 + y.
  3. So the mean is 1720+xy32+y\dfrac{1720 + xy}{32 + y}.

(b)

  1. Red then blue: 47×36=1242\frac47 \times \frac36 = \frac{12}{42}.
  2. Blue then red: 37×46=1242\frac37 \times \frac46 = \frac{12}{42}.
  3. Add: 2442=47\dfrac{24}{42} = \dfrac47.

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