Question

Suppose that each week you buy a ticket in a lottery which gives you a chance of 1/100 of a win. You do this each week for a year. Use a suitable Poisson distribution to estimate the chance that you get 2 wins during the year.

Answer 1

Solution Given data Total number of weeks in a year , n=52 let = The chance of winning a tottary in a week is ooot ( - 100 = oool=P P=0.01 X = The random Variable number of winnings in a year let x = The mean number of winning a lottery in a year equation @ then we get Now to substitute np values in = 52 X0.01 distribution x=0.52 x follows the Poisson We know that P(X=x) = x² Where x=0, 1, 2, 3 Now to find the probability that you get a wins during the year -052 12 p(x-2) = eost (ousa)² . P(x-2) = 0.5945 (0. 2104) 0.1608 = 0.0004 P(X=2) = -2 Therefore the probability that you get a wins during the year (0.0804]