Browse · MathNet
PrintChina Mathematical Competition
China statistics
Problem
Nine balls of the same size and color, numbered , were put into a packet. Now draws a ball from the packet, noted that it is of number , and puts back it. Then also draws a ball from the packet and noted that it is of number . Then the probability for the inequality to hold is ( ).
Solution
Since each has equally different possible results for and to draw a ball from the packet independently, the total number of possible events is .
From we get .
We find that when , can take any value in to make the inequality hold. Then we have admissible events.
When , can be , and there are admissible events.
When , can be , and there are admissible events.
When , can be , and there are admissible events.
When , can only be , and there is admissible event.
So the required probability is .
From we get .
We find that when , can take any value in to make the inequality hold. Then we have admissible events.
When , can be , and there are admissible events.
When , can be , and there are admissible events.
When , can be , and there are admissible events.
When , can only be , and there is admissible event.
So the required probability is .
Final answer
61/81
Techniques
Permutations