Teaching Kids Programming: Videos on Data Structures and Algorithms
You are given a dice, rolling 3 times one after another. what is the probability of obtaining numbers in strictly increasing order?
Probability of Rolling a Dice – Strictly Increasing Order using Math
First, we compute the probability of rolling 3 unique numbers one after another.
The first time, we have 100% probability, and the second time, it is 5 over 6, and the third one is 4 over 6. Thus:
Rolling a 3 unique digit has probability of
For each 3 digit, there are 6 permutations (3*2*1), and only 1 of them is strictly increasing, thus:
Probability of Rolling a Dice – Strictly Increasing Order is
Probability of Rolling a Dice – Strictly Increasing Order using Bruteforce/Simulation
We can bruteforce all possibilities of rolling a dice 3 times, and then count those with strictly increasing order:
1 2 3 4 5 6 7 8 9 | cnt = 0 for first in range(1, 7): for second in range(1, 7): for third in range(1, 7): if first < second < third: cnt += 1 total = 6*6*6 print(cnt/total) # print(1*(5/6)*(4/6)/6) |
cnt = 0 for first in range(1, 7): for second in range(1, 7): for third in range(1, 7): if first < second < third: cnt += 1 total = 6*6*6 print(cnt/total) # print(1*(5/6)*(4/6)/6)
Time and space complexity is O(1) constant as the problem scope is fixed. See also: Teaching Kids Programming – Probability of Two Sixes in a Row when Rolling a Dice Three Times (One After Another)
–EOF (The Ultimate Computing & Technology Blog) —
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