Two Blackjacks

Before dealing from a fresh deck of cards, the dealer offers you two bets: You can bet any amount that you will be dealt a blackjack, and you can bet any amount that the dealer will be dealt a blackjack. If either hand is dealt a blackjack, you will be paid 17-to-1 for the respective bet. If BOTH hands get a blackjack, both bets will be paid 20-to-1 (as long as you originally placed both bets; placing a single bet will only be paid 17-to-1). So a few questions in probabilities arise. Find the probabilities as reduced fractions of:
  1. One hand being dealt a blackjack from a freshly shuffled deck.
  2. Two hands being BOTH dealt blackjacks from a fresh deck.
  3. Neither of two hands being dealt a blackjack
A Blackjack is the combination of an Ace and one of [Ten, Jack, Queen, or King].

Source: Reader Rich Polster.

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