The probability that an individual is left handed is 0.11 In a class of 40 students what is the probability of finding five left handers?

Answer 1

If the probability of a person being left handed is .11, then the probability of a person being right handed is .89 (1.00 - .11). In a class of 40 people, there are 40! (40 factorial) = 40 x 39 x 38 x .... x 3 x 2 x 1 possible Permutations of students. Within this number, there are many that will yield exactly 5 left handed people. 40-P-5 is the number of Permutations of 5 within a class of 40 (sorry, can't use the correct formating here!): = 40! / (40 - 5) ! = 40! / 35! = 40 x 39 x 38 x 37 x 36 Since we don't care about order..... we need to factor out the number of identical permutations. 40-C-5 = 40-P-5 / 5! So.... (40 x 39 x 38 x 37 x 36) / (5 x 4 x 3 x 2 x 1) = 658,008 Now, what is the probability of any one such combination? (.89 to the power 35) x (.11 to the power 5) = 0.000000273 So the probability of exactly 5 left handed people in the class is 658,008 x .000000273 = 17.9408137 %