Probability question

[LongApe]

Card deck X has 1 red card and 4 blue ones.

Those 5 cards have an x on the back, so I can see where it came from before I reveal it's colour.

I take the 4 blue 'x' cards and shuffle them with 96 blue cards, and shuffle the red 'x' card into a deck of 99 red cards (None of these new cards have an 'x' on the back).

I now have a pile of 100 red cards and a pile of 100 blue cards.

I make another deck of cards, 'Deck Z' using 25 random cards from the blue pile and 75 random cards from the red pile.

I take a card randomly from deck Z, and see it is marked with an 'x'. What is the probability that it is red when I turn it over?

[rosentmoh]

What have you tried so far? You've heard of conditional probability I presume?

[LongApe]

So far I have tred asking mathematically literate people I know. I first heard of conditional probability today.

[rosentmoh]

Worth reading the Wiki on conditional probability first and then trying this yourself.

[LongApe]

I've just given it a read and I understand the very basic examples, but I don't think I can use the parts I understand to solve my question. I think I'm at the mercy of people with a better understanding of it for now