9780321989178 Recall thatto begineach player is dealt 2 card

Recall that,to begin,each player is dealt 2 cards face down, called\'\'hole cards\'\', from an ordinary deck of 52 playing cards, as pictured in Fig.4.3 on page 165.The best possible starting hand is two aces,referred to as \'\'pocket aces\'\'.The probability that you are dealt pocket aces is 1 /221,or 0.00452 to three significant digits. If you studied either Sections 4.5 and 4.6 or Section 4.8,verify that probability.Using the result from part(a),obtain the probability that you are dealt \'\'pocket kings.\'\'Using the result from part (a)and your analysis in part (b),find the probability that you are dealt a \'\'pocket pair,\'\' that is, two cards of the same denomination.

Solution

a)

There are 4C2 = 6 ways to choose 2 aces.

There are 52C2 = 1326 ways to choose any 2 cards.

hence,

P = 6/1326 = 1/221 [ANSWER]

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b)

THis is the same probability, because there are also 4 kings in a deck. Hence,

P = 1/221 [ANSWER]

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c)

There are 13 denominations to choose the pair from. Hence,

P = (1/221)*13 = 13/221 = 1/17 [ANSWER]