7. Aplia Hold \'Em Aa Aa Aplia Hold \'Em is a simplification of the popular poke

Question

7. Aplia Hold 'Em Aa Aa Aplia Hold 'Em is a simplification of the popular poker game Texas Hold Em. Aplia Hold 'Em is played with a special Aplia card deck that contains only six cards: the jack, queen, and king of diamonds and the jack, queen, and king of spades. Two players are each dealt two cards, face down. A fifth (common) card is dealt face down and subsequently tumed over so it is face up. Each player's hand consists of three cards: two private cards plus the common card. Each hand forms one of the following: a pair (two cards with the same face), a straight (a jack, queen, and king not all of the same suit), or a fush (all cards of the same suit). A nush beats a straight and pair; a straight beats a pair. Any straight ties any straight; any pair ties any pair. A game results in either a win by one of the players or a tie. You and an opponent are getting ready to play Aplia Hold 'Em, Five cards have been dealt from a well-shumed Aplia card deck, but you have not picked up your private cards, and the common card has not been tumed over The following graphic organizer represents the pre-play stage of the game. There are two parts to the graphic: a card bank and a poker table. Because the five dealt cards are shown face down on the poker table, you are uncertain of their values. However you know that the facedown cards are drawn from the cards in the card bank. aptia You Opponent Before play begins, the probability that your opponent's hand forms a flush is Now play begins. You pick up your private cards and see that you have the queen of spades and the king of spades. 32:35 Timeout

Explanation / Answer

Probability that opponent's hand forms a flush( includng straight and royal flush) is

13C5 * 4C1 /52C5 = 5148/2598960=0.00198

If we want to exclude royal and straight flush,subtract 40

P=5108/2598960=0.001965

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