Math, Speculation and Intuition

This is an important subject whenever faced with a news story or ad that tries to entice or scare you based on the chance you estimate events to be subject to.

Five decks of cards are arranged into two giant decks face down such that one is 70% diamonds and hearts while the other is 70% clubs and spades. You select one decks and draw 12 cards at random and find that 8 of the cards are red and 4 are black.

Question: what is the approximate likelihood that the deck you drew from is the deck that has mostly red cards?