Suppose you have a lottery ticket for soccer games The winni

Suppose you have a lottery ticket for soccer games. The winning ticket must have all 13 games correct. For each game, there may be three results. Team A wins, Team B wins, or a Draw. Lets assume that there is a 33% chance of each column (reasonable estimate since draws in soccer games are common). Each person playing the lottery is only allowed to put one result for each column. What is the probability of the person winning the lottery? How much would the probability increase if for one of the games, a person would be allowed to put two results?

Solution

P(winning lottery) = 1/3^13 = 0.00000062722547438631

Since the person can select 2 columns in any one position, we have to multiply (2/3) *(1/3)^12 = 0.00000125445094877261

Note that position of ticket for 2 columns is pre-decided, and is not random, and should not be taken in combination.