In the standard poker, there are 52 cards with four suits (diamond, club, heart and spade)...

 

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In the standard poker, there are 52 cards with four suits (diamond, club, heart and spade) where each suit contains 13 cards, which are numbered as 1 - 10, 11 (J), 12 (Q), and 13 (K). (a)How many different ways can we distribute these cards to three players where each player will get five cards? (b) Please calculate the minimum number of cards that we need to take from the standard deck of 52 cards to ensure the probability of obtaining at least two cards with the same suit exceeds 0.7. (c) Suppose that we pick a card randomly from the standard deck of 52 cards five times and each time the picked card is returned to the deck before the next pick. What is the probability of getting exactly two times of "diamond"? (d) Suppose that we pick a card randomly from the standard deck of 52 cards five times and each time the picked card is returned to the deck before the next pick. A random variable X is defined as the number of times that a red card (diamond or heart) is obtained. Please calculate the distribution of this random variable. In the standard poker, there are 52 cards with four suits (diamond, club, heart and spade) where each suit contains 13 cards, which are numbered as 1 - 10, 11 (J), 12 (Q), and 13 (K). (a)How many different ways can we distribute these cards to three players where each player will get five cards? (b) Please calculate the minimum number of cards that we need to take from the standard deck of 52 cards to ensure the probability of obtaining at least two cards with the same suit exceeds 0.7. (c) Suppose that we pick a card randomly from the standard deck of 52 cards five times and each time the picked card is returned to the deck before the next pick. What is the probability of getting exactly two times of "diamond"? (d) Suppose that we pick a card randomly from the standard deck of 52 cards five times and each time the picked card is returned to the deck before the next pick. A random variable X is defined as the number of times that a red card (diamond or heart) is obtained. Please calculate the distribution of this random variable.

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step 1 a Giving Three Players Their Cards Using a regular 52card deck we can determine how many options there are to deal five cards to each of three players by using the combination formula Number of ... View the full answer