A strange deck of cards

In a non-standard deck of cards there are

  • 20 blue cards (numbered 1 through 20),
  • 20 green cards (numbered 1 through 20), and

20 red cards (numbered 1 through 20)

Four cards are dealt without replacement from this deck.

  1. What is the probability that exactly two of the four cards dealt are blue?
  2. Given that at least one of the first two cards dealt is blue, what is the probability that exactly three of the four cards dealt are blue?
  3. What is the probability that at least two of the four cards dealt have the same numeric value (1 through 20)?

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