Teaching Kids Programming – Probability of Two Sixes in a Row when Rolling a Dice Three Times (One After Another)

Teaching Kids Programming: Videos on Data Structures and Algorithms

Rolling a dice three times one after another, what is the probability of having Two Sixes in a Row?

Rolling two sixes in a row can only be done in the following cases:

1. First and Second Six (third one not six):
2. Second and Third Six (first one not six):
3. Three Sixes: the probability is

Adding these cases to desired probability:

# 66? ==> (1/6)^2*(5/6)
# ?66 ==> (1/6)^2*(5/6)
# 666 ==> (1/6)^3

We can bruteforce since the total cases are 6*6*6 and then we count the cases when there are two consecutive sixes.

num = 0
total = pow(6, 3) # 6*6*6
for first in range(1, 7):
    for second in range(1, 7):
        for third in range(1, 7):
            if (first == second == 6) or (second == third == 6):
                num += 1
print(num/total)

O(1) constant complexity for time and space since the input size is fixed to 3 dices (constant loops, 216). See also: Teaching Kids Programming – Probability of Rolling a Dice: Strictly Increasing Order One After Another

–EOF (The Ultimate Computing & Technology Blog) —