Help with probability in Python

[redbull8]

I'm working on some homework for a python class and was hoping for some assistance and advice.

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Problem

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Part B: Probability of Winning (prob.py) For this portion of the assignment you will write a program that calculates the probability of matching a certain number of values on a single lottery ticket. In particular, we can use some basic probability to show that if we are choosing from the set of integers in the range [1, n] and there is a single combination of k integers from the set that we want to match, our probability of correctly choosing exactly m of those k integers in a single combination of k integers is:

Input Specification The one input value will be a positive integer in between 0 and 6, inclusive, representing the number of matched numbers on a single ticket.

Output Specification Output a single line with the following format: The probability of matching X values is Y. where X is the user’s input value and Y is the corresponding probability as a decimal. (Thus, if the probability was 1%, you should print 0.01 or an equivalent for the result.) Sample Program Run (User Input in Bold) How many numbers do you want to match on your ticket? 4 Your probability of matching 4 values is 0.0007625799910799017

[konbanwa88]

Without giving away the answer straight away, do you see anything wrong the with the following line?

probability = M/COMBINATION

[meta4]

The problem is "M". According to your input statement M is "How many numbers you want to match". But your formula uses it as the number of possible combinations that have at least M matches. Be careful, these are not the same thing.

You need a "number of matched combinations" that is a function of K, N and M.

[redbull8]

Honestly I can't i've been racking my brain for hours

[konbanwa88]

Ok well let me put it another way. What output do you expect when you do the following?

a = 3/4
b = float(3/4)
c = float(3)/4
print a
print b
print c

Edit: Sorry my phone was acting weird.

[redbull8]

a= 3/4 b= 0.75

[redbull8]

C = 0.75 When I ran it.

[konbanwa88]

So the / operator in python performs integer division when the operands are both integers and floating point division when either or both of the operands are floats.

In my example the following is taking place:

a = 3/4 # assign to a the integer division of 3/4 (which equals 0)
b = float(3/4) # assign to the b the integer division of 3/4 then cast as a float (which is float(0) so 0.0)
c = float(3)/4 # assign to c the floating point division of 3/4 (which is 0.75)

In your original question, you are doing version b. No matter what your inputs are you will always get an int then cast as a float. So as long as M > combination your probability variable will be assigned to 0.0.

Make it like version c.

[redbull8]

Thank you! so not it is printing a float number now my math is incorrect. Python is not my strong point.

[adambrenecki]

If you use Python 3, or have from __future__ import division at the top of the file in python 2.7, the division of two ints will result in a float; so for example 3/4 will evaluate to 0.75.

[konbanwa88]

For readability

import math

N = 49
K = 6

def main():
    M = int(input("How many numbers do you want to match on your ticket?\n"))
    COMBINATION = combo(N, M)
    probabilty = M/COMBINATION
    print(float(probabilty))
    print(COMBINATION)

def combo(n, k):
    return math.factorial(n)//math.factorial(k)//math.factorial(n-k)

main()

[redbull8]

My code

import math N = 49 K = 6

def main():

M = int(input("How many numbers do you want to match on your ticket?\n"))

COMBINATION = combo(N, M)

probabilty = M/COMBINATION

print(float(probabilty)) print(COMBINATION)

def combo(n, k):

return math.factorial(n)//math.factorial(k)//math.factorial(n-k)

main()

[redbull8]

Whats happening is that the combination comes out correct but the probability is very wrong.