We first of all calculate our sample size. The number of ways of generating two letter and four digits in a way that repeatition is allowed is: 26^2 x 10^4 = 676 x 10000 = 6,760,000. Therefore, there are 6,760,000 possible number combinations for the lottery.
Probability of winning the first prize = 1/6,760,000 Probability of winning the second prize is 2/6,760,000 = 1/3,380,000 Probability of winning the third prize is 10/6,760,000 = 1/676,000 Probability of winning nothing is (6,760,000 - 13)/6,760,000 = 6,759,987/6,760,000 *[there are 13 winnings in all]
Expected winning from the lottery = (1/6,760,000) x (100,000 - 0.33) + (1/3,380,000) x (50,000 - 0.33) + (1/676,000) x (1,000 - 0.33) + (6,759,987/6,760,000) x (-0.33) = 0.0148 + 0.0148 + 0.0015 - 0.3300 = -0.30
Therefore, the expected winning is a loss of 30 cents. This means that it is not worth 33 cents to enter this lottery.
When factorising a quadratic, the product of the two factors should equal the constant term (12), and the sum of the two factors should equal the linear term (7). To find the two factors, list out the factors of 12 (1x12, 2x6, 3x4) and identify the pair that adds up to 7 (3+4).
An alternative method if you get stuck during your exam would be to solve it algebraically using the quadratic formula and then write it in the factorised form.
a = (-7 +or- sqrt(7^2 - 4(1)(12)) / 2(1)
= (-7 +or- sqrt(1))/2
= -3 or -4
These factors are the negative of the values that would go in the brackets when written in factorised form, as when a = -3 the factor (a+3) would equal 0. (If it were positive 3 instead, then in the factorised form it would be a-3).
<u>Question 10</u>
-3(x - y)/9 + (4x - 7y)/2 - (x + y)/18
Rewrite each fraction with a common denominator so you can combine the fractions into one.
