How likely is it to pick 10 red b***s consecutively, assuming random and uninformed selection; from a bag containing 10 each of red, white and blue b***s?
Do you mean pick the b***s with replacement (put each one back after selecting it)
Or without replacement (leave each ball out after it is selected)
With replacement:
Each time you pick a ball=10 red b***s/30 total b***s, of picking a red ball. That equals 1/3.
Since you're computing the chance that you would do that 10 times in the row, that would be 1/3*3*3*3*3*3*3*3*3*3=1/310=1/59049.
Without replacement:
You're computing the chance that you would pick all ten red b***s. The first time you pick, you have a 10/30=1/3 chance of picking a red ball. If you do get a red ball, the second time you pick, you have a 9/29 (since one ball was removed) chance of pikcing a red, the third time 8/28, the fourth... and the tenth 1/21. Multiply those together to get: 3628800/109027350432000=1/30045015=0.0000000332833916
Note that even if you pick some other b***s first, say all of the other 20 b***s before you come up with a red (20/30*19/29*18/28...*1/11), you would still get the same answer. This implies that even if you do pick some other b***s first, you'll still get that answer.
Do you mean pick the b***s with replacement (put each one back after selecting it)
Or without replacement (leave each ball out after it is selected)
With replacement:
Each time you pick a ball=10 red b***s/30 total b***s, of picking a red ball. That equals 1/3.
Since you're computing the chance that you would do that 10 times in the row, that would be 1/3*3*3*3*3*3*3*3*3*3=1/310=1/59049.
Without replacement:
You're computing the chance that you would pick all ten red b***s. The first time you pick, you have a 10/30=1/3 chance of picking a red ball. If you do get a red ball, the second time you pick, you have a 9/29 (since one ball was removed) chance of pikcing a red, the third time 8/28, the fourth... and the tenth 1/21. Multiply those together to get: 3628800/109027350432000=1/30045015=0.0000000332833916
Note that even if you pick some other b***s first, say all of the other 20 b***s before you come up with a red (20/30*19/29*18/28...*1/11), you would still get the same answer. This implies that even if you do pick some other b***s first, you'll still get that answer.
