Andy C. answered • 05/27/18

Tutor

4.9
(27)
Math/Physics Tutor

NAIVELY,

Probability of 1 win = 1 - Probability of zero wins

That is, the probability of winning the prize equals 1 minus the probability of losing.

Since you have 90 tickets, the probability of losing on the first pick is 1359910/1360000

Since the winning tickets are disqualified from winning again, the numerator and denominator

are reduced by an average of 68 after each pick.

So we are interested in the sum of the infinite series:

1 - SUM [90/(1360000-68*N)] , N=0,1,2,3,.....,5000

which is a finite arithmetic sequence

The formula is Sn = N( A1+An)/2 where N is the number of terms, A1 is the first term, and An is the last term

The first term is 90/1360000 = 9/136000

The 5000th term is 90/(1360000-68*5000) = 90/1020000 = 9/102000 = 3/34000 = 12/136000

The partial sum is then Sn = 5000*(9/136000 + 12/136000)/2 = 2500*21/136000 = 0.386029411764705882359....

Dave S.

If I replace the 90 tickets with 68 tickets so I now have the same tickets as everyone else the equation you have provided gives me a probability of 29.2%, but my logic tells me that with 20,000 people and 5,000 different winners all with the same odds of winning the probability of anyone including me should be 25%

05/27/18