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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 which is 7.7%. (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 13x + 4y + 5z = 72  => Eq. 2x + z = 8  => Eq. 3 Find the values of x, y and z. From Equation 3: If x + z = 8Then x = 8 – zSubstituting the value of x in either 1 or 2Say Eq. 1:8 – z + y + z = 188 + y = 18 (z is eliminated)y = 18 – 8 = 10Substituting the values of x and y in 23(8 – z) + 4(10) + 5z = 7224 -3z + 40 + 5z = 722z = 72 – 24 – 40 = 72 – 642z = 8z = 4x = 8 – 4 = 4 Therefore, x = 4, y = 10 and z = 4

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