I draw card x out of a deck of 78 cards. What is the probability that I will draw card x again before my sixth draw?

Question

To clarify, say I draw a card labeled "green" out of a deck of 78 other cards, none of which are the same.

 

I draw four more times after that, and on my fifth draw, I receive "green" again. What are the odds of that happening, exactly?

Answer 1

This has to be with replacement, otherwise X (which is unique) is not possible after obtained on first draw.

Then you need to calculate several individual probabilities and add them together to get P(X on draw # 2, 3, 4 or 5)"

 

P(X on 2nd)

P(no X on 2nd, but X on 3rd)

P(no X, no X, but X on 4th draw)

P(no X, no X, no X, but X on 5th).

 

Have fun.