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Examples and Solutions

Probability: (i) What is the probability of drawing an ace from a well shuffled deck of cards?
Since there are 52 cards in the deck and there are only 4 aces, the probability of drawing an ace is 4/52 or 1/13.

(ii) In a bag there are 6 blue marbles, 4 red and 3 green. If the bag is shaken, what is the probability that a red marble will be drawn?
Total number of marbles in the bag is 13. Probability of drawing a red is 4/13.

Compound Interest: If $1,000.00 is invested at 5% compounded annually, how much will be in the account at the end of 3 years?
Applying the formula A = P(1 + i) ͭ  and substituting the values for P = 1000, i = 0.05 and t = 3
Amount = A = 1000(1 + 0.05)

A = 1000(1.05) = 1000(1.1576) = 1157.63

Amount in the account at the end of the 3 year period is $1,157.63

 Equations with 3 unknowns:
 x + y  + z = 18  => Equation 1
 3x + 4y + 5z = 72  => Eq. 2
 x + z = 8  => Eq. 3

 Find the values of x, y and z.

From Equation 3: 
If x + z = 8
      Then x = 8 z
Substituting the value of x in either 1 or 2
Say Eq. 1:
8 z + y + z = 18
                                   8 + y = 18 (z is eliminated)
                             y = 18 8 = 10
Substituting the values of x and y in 2
3(8 z) + 4(10) + 5z = 72
     24 -3z + 40 + 5z = 72
          2z = 72 24 40 = 72 64
                       2z = 8
                         z = 4
                                   x = 8 4 = 4

    Therefore, x = 4, y = 10 and z = 4
values of x, y and


 Ratio and Proportions: $30.00 is shared among three people in the ratio 1:8:11.  
 Calculate (i) the smallest share, (ii) the largest share.
 Let's consider the ratio as three parts of a whole. The whole of the three parts then would be  
 1+8+11 = 20.
 The smallest share now is 1 out of 20 times 30 = (1/20) X 30 = 3/2 = 1.5 = $1.50
 The largest share is (11/20) X 30 = 33/2 = 16.5 = $16.50

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