There is no escape...believe it or not. Mathematics is everywhere.
We have 4 decks of cards, and each deck is missing a different suit:
1. D(R), S(B), C(B)
2. H(R), S(B), C(B)
3. H(R), D(R), C(B)
4. H(R), D(R), S(B)
H(R) represents Hearts(Red). There are 39 (3x13) cards in each deck.
We pick one deck at random, then we draw two cards at random from that deck.
On turning over the two cards, we see that they are both Red (Hearts or Diamonds).
Which deck did we pick (1,2,3 or 4), and how certain are you of that?
We have two weighted coins.
One coin (H) has a 2/3 chance of landing heads-up.
The other coin (T) has a 2/3 chance of landing tails-up.
We pick one of these coins at random, leaving the other coin aside.
(a) On the first toss it lands heads-up. What is the probability that it is coin H.
(b) On the second toss it also lands heads-up. What is the probability that it is coin H.