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Probability, roll of a dice?
What is the probability that rolling a fair 20 face dice twice, the second number is bigger than the first one?
2 Answers
- ?Lv 74 years agoFavorite Answer
Prob(both numbers are the same) = 1/20
Prob(both numbers are different) = 19/20
In half the cases where numbers are different, 1st number will be greater than 2nd number, and in the other half, 2nd number will be greater than 1st number.
Prob(2nd number > 1st number) = 1/2 * (19/20) = 19/40
- 4 years ago
You have a 1-in-20 chance of rolling any particular number on your first roll
Then you have a decreasing chance of rolling a higher number: 19/20 , 18/20 , 17/20 , 16/20 , .... , 1/20 , 0/20
(1/20) * (19/20) + (1/20) * (18/20) + .... + (1/20) * (1/20) + (1/20) * (0/20) =>
(1/20) * (19/20 + 18/20 + 17/20 + ... + 1/20) =>
(1/20) * (1/20) * (19 + 18 + 17 + ... + 1) =>
(1/400) * (19/2) * (1 + 19) =>
(1/400) * (19/2) * 20 =>
(1/20) * (19/2) =>
19/40
20/40 = 0.5
1/40 = 0.025
19/40 = 20/40 - 1/40 = 0.5 - 0.025 = 0.475
You have a 47.5% chance of rolling a higher number with the 2nd roll.
