SOLUTION: Tickets are numbered 1 to 50 and placed in a box. Three tickets are drawn at random without replacement. What is the probability that their numbers are all greater than 25?

Click here to see ALL problems on Probability-and-statistics

Question 41634: Tickets are numbered 1 to 50 and placed in a box. Three tickets are drawn at random without replacement. What is the probability that their numbers are all greater than 25?
Found 2 solutions by Nate, blacksaibot:
Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
There are 24 numbers that are greater than 25 in the box.
(24/50)(23/49)(22/48) = 12144/117600 = 1012/9800 = 506/4900 = 253/2450
About 10.33%

Answer by blacksaibot(4) (Show Source):
You can put this solution on YOUR website!
Nate, you are close but VERY WRONG!

There are TWENTY-FIVE numbers that are greater than 25.
count 26 to 50 and you get 25. NOT 24.

Think about it in smaller terms; if you have 10 cards numbered 1 through 10, how many are greater than 5? The answer isn't 4. 6,7,8,9,10 that's FIVE numbers.

Take the problem one step at a time.

First choice:
You have 25 out of 50 chances to get a number greater than 25.

Second choice:
No replacement, so now you have 49 tickets left.
So now you have 24 out of 49 chances to get a number greater than 25.

Third choice:
No replacement, so now you have 48 tickets left.
So now you have 23/48 chances to get a number greater than 25.

Multiply all three;
(25/50) * (24/49) * (23/48) = 23/196