7. +1 points WaneFMAC7 84.021 My Notes Ask Your Teacher Calculate the probabilit

Question

7. +1 points WaneFMAC7 84.021 My Notes Ask Your Teacher Calculate the probability of being dealt the following poker hand. (Recthat a poker player is dealt 5 cards at random from a standard deck of 52.) Express your answer as a decimal rounded to four decimal places. HINT [See Example 3.] Two pairs: Two cards with one denomination, two with another, and one with a third. Exampie: 34, 3v,Q4, Qv,J 8. -13 points WaneFMAC7 84.029. My Notes Ask Your The Sorry State Lottery requires you to select five different numbers from 0 through 59. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.) What is the probability of being a Big Winner? What is the probability of being a Small-Fry Winner? What is the probability that you are either a Big Winner or a Small-Fry Winner?

Explanation / Answer

Solution:-

7) Probability of two pairs = 0.047539

This hand has the pattern AABBC where A, B, and C are from distinct kinds.

The number of such hands = 13C2 × 4C2 × 4C2 ×11C1 × 4C1 = 123,552

Total number of combinations of different hands = 52C5 = 2,598,960

Probability of two pairs = 123,552/2,598,960 = 0.047539

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