In-a-card-game-for-four-players-a-pack-of-fifty-two-cards-is-dealt-round-so-that-each-player-receives-thirteen-cards-A-hand-that-contains-no-card-greater-than-nine-is-call

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Question Number 103223 by Ar Brandon last updated on 13/Jul/20

$$\mathrm{In}\mathrm{a}\mathrm{card}\mathrm{game}\mathrm{for}\mathrm{four}\mathrm{players},\mathrm{a}\mathrm{pack}\mathrm{of}\mathrm{fifty}-\mathrm{two}\mathrm{cards}\mathrm{is}\mathrm{dealt}\mathrm{round}\mathrm{so}$$$$\mathrm{that}\mathrm{each}\mathrm{player}\mathrm{receives}\mathrm{thirteen}\mathrm{cards}.\mathrm{A}\mathrm{hand}\mathrm{that}\mathrm{contains}\mathrm{no}\mathrm{card}\mathrm{greater}\mathrm{than}$$$$\mathrm{nine}\mathrm{is}\mathrm{called}\mathrm{a}\mathrm{yarborough}.\mathrm{How}\mathrm{many}\mathrm{deals}\mathrm{are}\mathrm{necessary}\mathrm{for}\mathrm{the}\mathrm{probability}$$$$\mathrm{of}\mathrm{at}\mathrm{least}\mathrm{one}\mathrm{hand}\mathrm{being}\mathrm{a}\mathrm{yarborough}\mathrm{to}\mathrm{be}\mathrm{greater}\mathrm{than}\frac{1}{2}?\left(\mathrm{Ace}\mathrm{ranks}\mathrm{high}\right)$$

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