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WAEC 2020 · Paper 2 · Q5

Number 1 2 3 4 5 6
Outcomes 32 mm 25 40 28 45

A die was rolled a number of times. The outcomes are as shown in the table. If the probability of obtaining 2 is 0.15, find the:

  1. (a)

    value of mm;

  2. (b)

    number of times the die was rolled;

  3. (c)

    probability of obtaining an even number.

Worked solution (try it first)

(a)

  1. The total number of rolls is 32+m+25+40+28+45=170+m32 + m + 25 + 40 + 28 + 45 = 170 + m.
  2. So P(2)=m170+m=0.15P(2) = \frac{m}{170 + m} = 0.15.
  3. Then m=0.15(170+m)=25.5+0.15mm = 0.15(170 + m) = 25.5 + 0.15m, so 0.85m=25.50.85m = 25.5 and m=30m = 30.

(b)

  1. The die was rolled 170+30=200170 + 30 = 200 times.

(c)

  1. Even numbers are 2, 4 and 6: 30+40+45=11530 + 40 + 45 = 115 outcomes.
  2. P(even)=115200P(\text{even}) = \frac{115}{200}
    =2340= \frac{23}{40}.

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