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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 = 3Amount = A = 1000(1 + 0.05)³ A = 1000(1.05)³ = 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 = 4values 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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