Python code for finding the probability of sum of numbers on two dies rolled

Q. No. 2 :

Two dice are rolled. We define s as the sum of the values on the two faces. 

(a) What is the mean (expected value) of s? 

(b) What is the probability that s is even? 

Answer :

(a) 
Mean is the average value. 
Each die can have a value 1 to 6. 
Hence the sum can be 2 to 12.
11
12
13
14
15
16
21
22
23
24
25
.... 
....
....
64
65
66
Hence there are 36 possible combinations.
The total sum can be 252.
Hence the mean is 252/36 = 7

The python code is given below :

n = 0
sum=0
for first in range(1,7):
    for second in range(1,7):
        sum+=int(first)+int(second)
        n+=1
print (int(sum)/n) 

(b)

The answer to this problem is rather simple. Among the total combinations possible, half are odd and half are even (As the numbers are sequentially increasing). Hence, the answer is 1/2 = 0.5

sum=0
n=0
tries=0
for first in range(1,7):
    for second in range(1,7):
        sum=int(first)+int(second)
        if sum%2 ==0 :
            n+=1
        tries+=1
print(int(n)/tries)

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