if choosing one number from 0 to 100 randomly.
find the probability that a number chosen is of last digit is greater than first digit of two number
take a look:
12 ... 19: 8
23 ... 29: 7
...
89: 1
so there are 1+2+3...+8 = 8*9/2 = 36
so P = 36/101
I didn't understand dear
To find the probability that the last digit of a randomly chosen number is greater than the first digit of the number, we can break down the problem into cases and calculate the probability for each case.
Case 1: First digit and last digit are both 0.
In this case, there is only one number, which is 0. The last digit is not greater than the first digit. Therefore, the probability is 0 for this case.
Case 2: First digit is 0 and last digit is between 1 and 9.
In this case, there are 9 possible numbers (10, 20, 30, ..., 90) where the last digit is greater than the first digit. Since there are a total of 10 numbers (0, 10, 20, ..., 90) with a first digit of 0, the probability for this case is 9/10.
Case 3: First digit is between 1 and 8 and last digit is between 0 and 9.
In this case, both the first and last digits have 9 possible values each. So, there are a total of 81 possible numbers (10, 11, 12, ..., 89) where the last digit is greater than the first digit. There are 81 possible numbers (10, 11, 12, ..., 99) with first digit between 1 and 8. Therefore, the probability for this case is 81/81 = 1.
Case 4: First digit is 9 and last digit is between 0 and 8.
In this case, there are 9 possible numbers (90, 91, 92, ..., 98) where the last digit is greater than the first digit. There are 9 possible numbers (90, 91, 92, ..., 99) with a first digit of 9. Therefore, the probability for this case is 9/9 = 1.
So, the total probability is the sum of the probabilities for each case:
Probability = probability of case 1 + probability of case 2 + probability of case 3 + probability of case 4
= 0 + 9/10 + 1 + 1
= 11/10
However, the probability should be between 0 and 1. Since the resulting probability is greater than 1, there may be a mistake in the problem statement or the calculation. Please check the problem statement or clarify any additional details if needed.