What is the probability of getting nothing for 40 consecutive hands and then get

Question

What is the probability of getting nothing for 40 consecutive hands and then getting a Straight Flash? What would your profit be?
What is the probability of getting nothing for 40 consecutive hands? A popular casino table game is Three-Card Poker. One aspect of the game is the " pair-plus" bet in which a player is paid a dollar amount for any hand of a pair or better, regardless of what the dealer has. The table shows the profit and probability of the various hands of a player playing the $5 pair plus bet. Outcome Profit Probability Straight Flush 200 12/5525 Three of a Kind 150 1/425 Straight Flush Pair Nothing 36/1105 274/5525 72/425 822/1105 30 20

Explanation / Answer

c)

probability of getting nothing 40 consecutive hands = (822/1105)^40

= 0.00000725072

d)

probability of getting nothing 40 consecutive hands and straight flash = (822/1105)^40 * 12/5525 = 1.57481863e-8

profit = -5 *40 + 200 = 0

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