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.
