Suppose that we count the number of weeks in a year that the

Suppose that we count the number of weeks in a year that the weekly state Lotto has a winner. Assume that this process is a Bernoulli counting process with frame size one week and probability of a winner p=0.7. Suppose the prize is 1,000,000 the first week and doubles by this amount each week that there is no winner. Simulate the Lotto over three years\' time and determine the largest amount of prize money available during any given week

Solution

Probability of winning is 0.7.

There are 52 weeks in a year. Therefore, in 3 year no. of weeks = 3* 52 = 156

Therefore no. of times weekly state lotto will have a winner in three years = 156* 0.7 = 109.2

The price money will rise if there is no winner.

The no.of times there is no winner in 3 years = 156 - 109.2 = 46.8

Starting amount = 1000000 .

Therefore amount in next week there is no winner = 2000000.

Therefore the largest amount of prize money available during any given week = 1000000 * 2 ^46.8-1

= 6.125954988 * 10¹⁹