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The sponsors of a well-known charity came up with a unique idea to attract wealthy patrons to the $ 500 a plate dinner. After the dinner, it was announced that each patron attending could buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays is 50-50. If you bought a set of 20 tickets, what is the chance that you will win 15 or more prizes?
Correct Answer: C
This is a binomial probability. The probability of getting r successes out of n trials where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p) is given by: r (n-r) n!(p )[q ]/r!(n-r)!. Here n = 20, p = 0.5 and q = 0.5 and r = 15,16,17,18,19,20. Therefore we have 15 5 P(15) = 20!(0.5 )(0.5 )/15!5! = 0.0148 16 4 P(16) = 20!(0.5 )(0.5 )/16!4! = 0.0046 P(17) = 0.0011 P(18) = 0.0002 P(19) = 0.00002 P(20) = 0.000001 The sum adds up to 0.0207.