Lottery probability Python code

Question

I’m working on a code to solve this problem:

You and your friends are in New York and are planning to go see a Broadway musical. Unfortunately, New York being New York, the tickets are just a tiny bit expensive. But one of the shows has a ticket lottery each night where impecunious people such as you have a chance to win the right to buy slightly less expensive tickets to good seats. The lottery operates as follows. First, everyone interested enters the lottery. Then, n lucky winners are drawn, and each of these is offered to buy up to t tickets.

Given the number of people p in your group (all of which entered the lottery) and the total number of people m that entered the lottery, what is the probability that you will be able to get tickets for your entire group? Assume that the n lucky winners are chosen uniformly at random from the m people that entered the lottery, and that each person can win at most once.

Here’s my code:

import math

def lottery():

    m = int(raw_input('The number of people who entered the lottery: '))
    n = int(raw_input('The number of winner drawn from the total: '))
    t = int(raw_input('The number of tickets each winner can purchase: '))
    p = int(raw_input('The number of people in your group: '))

    def combinations(n, k):
        if 0 <= k <= n:
            ntok = 1
            ktok = 1
            for t in xrange(1, min(k, n - k) + 1):
                ntok *= n
                ktok *= t
                n -= 1
            return ntok // ktok
        else:
            return 0

    needed_wins = int(math.ceil(p/t))

    others = m - p

    loss = 0
    for i in range(needed_wins):
        loss += combinations(others, n-i) * combinations(p, i)

    total = combinations(m, n)

    prob = 1 - loss / total

    print(prob)

I tried to run it but the result came out wrong. For example, if the combination is (100,10,2,1), the result should be 0.1; instead it returned 1. I really appreciate it if anyone can help me out here.

Asked By: Long Pham

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Source

Answer 1

In Python 2, when you divide two integers, you always get an integer result. Try adding this line to the top of the file, which will get you the new Python 3 behavior, where dividing ints produces floats:

from __future__ import division

Answered By: Ned Batchelder

Answer 2

import math

def lottery(m, n, t, p):

  needed_wins = math.ceil(p/t)

  others = m - p

  loss = 0
  for i in range(needed_wins):
    comb_others = combinations(others, n-i)
    comb_group = combinations(p, i)
    loss += comb_others * comb_group

  total = combinations(m, n)

  prob = 1 - loss / total

  return prob


def combinations(n, k):
  if 0 <= k <= n:
    ntok = 1 
    ktok = 1
    for t in range(1, min(k, n - k) + 1):
      ntok *= n
      ktok *= t
      n -= 1
    return ntok // ktok
  else:
    return 0

Answered By: Jose Perez

Lottery probability Python code

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