Question

# A) A poker hand consists of five cards randomly dealt from a standard deck of 52...

A) A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places.

Determine the probability that exactly 4 of these cards are Aces.

Determine the probability that all five of these cards are Spades.

Determine the probability that exactly 4 of these cards are face cards.

Determine the probability of selecting exactly 2 Aces and exactly 2 Kings

Determine the probability of selecting exactly 1 Jack.

B)Jenelle draws one from a standard deck of 52 cards.

1. Determine the probability of drawing either a jack or a ten?
Write your answer as a reduced fraction.
1. Determine the probability of drawing either a jack or a club?
Write your answer as a reduced fraction.

c)The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs \$4. There is 1 winning ticket out of the 210 tickets sold. The winner gets a prize worth \$94. Round your answers to the nearest cent.

What is the expected value (to you) of one raffle ticket? \$

Calculate the expected value (to you) if you purchase 8 raffle tickets. \$

What is the expected value (to the PTO) of one raffle ticket? \$

If the PTO sells all 210 raffle tickets, how much money can they expect to raise for the classroom supplies? \$

A)

1) probability that exactly 4 of these cards are Aces=4C4*48C1/52C5 = 0.000018 or 0.0018%

2)  probability that all five of these cards are Spades. = 13C5/52C5 = 0.000495 or 0.0495%

3) probability that exactly 4 of these cards are face cards = 12C4*40C1/52C5 = 0.007618 or 0.7618%

4) probability of selecting exactly 2 Aces and exactly 2 Kings = 4C2*4C2*44C1/52C1 = 0.000609 or 0.0609%

5)  probability of selecting exactly 1 Jack = 4C1*48C4/52C5 = 29.9474%

B)

1)  probability of drawing either a jack or a ten = (4+4)/52 = 8/52 = 2/13

2) probability of drawing either a jack or a club = (4+13-1)/52=16/52=4/13

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