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?
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A. B. C. D. E.A
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: n!(p^r)[q^(n-r)]/r!(n-r)!. Here n = 20, p = 0.5 and q = 0.5 and r = 15,16,17,18,19,20. Therefore we have
P(15) = 20!(0.5^15)(0.5^5)/15!5! = 0.0148
P(16) = 20!(0.5^16)(0.5^4)/16!4! = 0.0046
P(17) = 20!(0.5^17)(0.5^3)/17!3! = 0.0011
P(18) = 20!(0.5^18)(0.5^2)/18!2! = 0.0002
P(19) = 20!(0.5^19)(0.5^1)/19!1! = 0.00002
P(20) = 20!(0.5^20)(0.5^0)/20!0! = 0.000001
The sum adds up to 0.207.