Answer to Question #74867 in Statistics and Probability for bob

Question

Compute the probability to pick a 2 digit number greater than 19, and 4 digit number where digits can't be repeated

Answer 1

There are 90 2-digit numbers:99-9=90.
There are 80 2 digit numbers greater than 19:99-19=80.
The probability to pick a 2 digit number greater than 19
P=80/90=8/9

There are 9000 4 digit numbers:9999-999=9000.
To construct a 4 digit number consisting of distinct digits we have 9 ways to choose the first digit (we can’t pick 0), 9 ways to choose the second (we can’t repeat the first) then 8 and 7 ways to choose the last two without repetition. Using the multiplication rule, we find that there are (9)(9)(8)(7) = 4536 numbers in the list that have distinct digits.
The probability to pick a 4 digit number where digits can't be repeated
P=4536/9000=63/125=0.504