Hi all, I refer to Tickbox Quiz #15 Q2. I don’t understand how the probability of taking out a ball without replacement for a particular ball is the same, no matter which attempt it is at? Greg explained it in his explanation video, but it’s still very confusing to me.
Shouldn’t it increase with lesser balls since there are fewer number of balls in contention? Will appreciate any help on this, thanks!
If this is the question you are referring to :
Its quite an enlightening experience when you understand why the probability remains the same.
So when you say the probability should increase since there are fewer balls in contention, you are actually thinking in your head the probability given 6 balls have been pulled already, and they were all not purple. You are thinking of a GIVEN probabilty. In other words, GIVEN that 6 non-purple balls have already been pulled, the probability of getting a ball purple is indeed higher.
You could think of it this way. You want to arrange 4 Ps, 3 Rs, and 5 Gs to form a 12 letter word. Now what is the probability that the 3rd letter is P? What is the probability that the 7th letter is P? Aren’t the probabilities the same?
I think in greg’s explanation he even shows all the possible cases and counts the cases to show that the probability remains the same regardless of 3rd or 7th pull.
Your example with the arrangement of letters was very useful. I get it now, thanks!
Hi Tushar,
I have a question.
In your explanation, the probability that the 3rd letter is P is 4/12 = 1/3.
But my thinking is a bit different. In case one P is placed in the 1st letter, the probability that the 3rd letter is P is decreased to 3/12.
Similarly, in case two Ps are placed in the 1st and 2nd letters, the probability that the 3rd letter is P is decreased to 2/12.
So, where am I wrong? I have not got it clear in my mind.
Hope you can help.
Many thanks.
I have solved this considering all possible cases for example: the desired purple draw is the first purple, the second purple, the third purple or the fourth purple (in the case of Quantity B). But my probabilities are not equal. Using combinations and letters, but that considered all 12 balls which is not the same as what the question is asking.
