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.
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