Question

Hello.

Below is a question that needs to be solved with Python.

Q. Suppose that you roll four 6-sided dice. Estimate the probabily that the die rolls are such that the four dice can be paired off so that one pair sums to 7 and the other sums to 9.

Here, I need 3 things.

a) Introdution - The Basic understanding of the problem.

b) Analysis - Explanation of the algorithm and display of the code that solves the problem.

b) Conclusion - Determine the solution of the problem and briefly discuss any potential generalizations.

please kindly show the solution clearly (Maybe with a screenshot of it too)

Thank you!

Answer 1

Basic Understanding Of The Problem

First of all, we have to check the pair of dice which will give sum 7.

There are 6 number of ways for getting the sum of pair of dice as 7. They are:

1 - 6

2 - 5

3 - 4

4 - 3

5 - 2

6 - 1

Next, we have to check the pair of dice which will give sum 9.

There are 4 number of ways for getting the sum of pair of dice as 9. They are:

3 - 6

4 - 5

5 - 4

6 - 3

It is given that the dice is 6-sided. So, for 1 dice, total probability of getting any values is 6. So, for a pair of dice, total probability of getting any values is 6*6=36.

Therefore, the probability of pair of dice to give sum as 7 = 6/36= 1/6

The probability of pair of dice to give sum as 9 = 4/36= 1/9

Since the first pair of dice should give sum as 7 AND the second pair of dice should give sum as 9, we have to add both probabilities.

That is, 1/6 + 1/9 = 5/18

Analysis

Algorithm

1. Start

2.For i =1 to 6

2.1.For j=1 to 6

2.2 If i+j =7 then

2.2.1. flag1 = flag1 +1

3.For i =1 to 6

3.1.For j=1 to 6

3.2 If i+j =9 then

3.2.1. flag2 = flag2 + 1

4. Print the Probability by adding flag1+flag2

5.Stop

Program

flag1=0 #inistialised variables with 0
flag2=0

for i in range(1,7):
for j in range(1,7):
if i+j == 7:
flag1=flag1+1 #checking if the sum of first pairs of dice is 7 and incrementing flag1
  
  
for i in range(1,7):
for j in range(1,7):
if i+j == 9:
flag2=flag2+1 #checking if the sum of first pairs of dice is 9 and incrementing flag2
  

#Output

print ("Probability of pair of dice with sum 7 = ",flag1,"/36")
print("Probability of pair of dice with sum 9 =",flag2,"/36")

print("Total Probability =", flag1+flag2,"/36")

Output

Probability of pair of dice with sum 7 = 6 /36

Probability of pair of dice with sum 9 = 4 /36

Total Probability = 10 /36

Generalised Program

I have also created an altered program where you can do the same with different numbers.

Example

Note: Probability should be always be in its least divisible form.That is, for above answer 9/36, it should be 1/4.