1. Five cards are dealt at random from a well-shuffled deck of 52 playing cards. Find...

1. Five cards are dealt at random from a well-shuffled deck of 52 playing cards. Find the probability that: a. All are spades. b. Exactly two are hearts. c. Exactly three are clubs. d. All are red. e. At least one card is ace. 2. Tossing a coin 15 times find the probability of getting exactly 4 tails. 3. Find the probability of getting at least 4 tails for tossing a coin 15 times

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orchestra answered 1 year ago

You are dealt a hand of five cards from a standard deck of 52 playing cards....

You are dealt a hand of five cards from a standard deck of 52 playing cards. Calculate the probability of the given type of hand. (None of them is a recognized poker hand.) (a) Mixed royal meeting: One of each type or royal card (king, queen, jack, ace) of different suites, and a last non-royal card (neither king, queen, jack or ace). Enter a formula. Examples: C(5,3)C(33,3)/C(14,2) C(5,3)C(33,3)C(4,1)/C(100,100) (b) Red and black double royal wedding: A red king, a red...

You are dealt a hand of five cards from a standard deck of 52 playing cards....

You are dealt a hand of five cards from a standard deck of 52 playing cards. Calculate the probability of the given type of hand. (None of them is a recognized poker hand.) 1. Double royal interracial wedding: Two kings of one color, two queens of the other color, and a last non-royal card (neither king, queen, jack or ace). Solve using a formula. Examples: C(5,3)C(33,3)/C(14,2) or C(5,3)C(33,3)C(4,1)/C(100,100)

A poker hand (5 cards) is dealt off the top of a well-shuffled deck of 52...

A poker hand (5 cards) is dealt off the top of a well-shuffled deck of 52 cards. Let X be the number of diamonds in the hand. Let Y be the number of hearts in the hand. 1. Do you think Cov[X,Y] is positive, negative, or zero? Explain. 2. let Di(i=1,...,5) be a random variable that is 1 if the ith card is a diamond and 0 otherwise. What is E[Di]? 3. let Hi(i=1,...,5) be a random variable that is...

1. Two cards are drawn from a well-shuffled ordinary deck of 52 cards. Find the probability...

1. Two cards are drawn from a well-shuffled ordinary deck of 52 cards. Find the probability that they are both aces if the first card is (a) replaced, (b) not replaced. 2. Find the probability of a 4 turning up at least once in two tosses of a fair die. 3. One bag contains 4 white balls and 2 black balls; another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the...

A 5-card hand is dealt from a perfectly shuffled deck of playing cards. What is the...

A 5-card hand is dealt from a perfectly shuffled deck of playing cards. What is the probability of each of the following events: a) The hand has at least one club b) The hand has at least two cards with the same rank c) The hand has exactly one club or exactly one spade d) The hand has at least one club or at least one spade

A standard deck of 52 cards is shuffled and dealt. Let X1 be the number of...

A standard deck of 52 cards is shuffled and dealt. Let X1 be the number of cards appearing before the first ace, X2 the number of cards between the first and second ace (not counting either ace), X3 the number between the second and third ace, X4 the number between the third and forth ace, and X5 the number after the last ace. It can be shown that each of these random variables Xi had the same distribution, i=1,2,...,5, and...

A hand of 13 cards is dealt from a standard deck of 52 playing cards. What...

A hand of 13 cards is dealt from a standard deck of 52 playing cards. What is the probability that it contains more spades (♠) than hearts (♡) given that the hand contains at least two spades?

Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so...

Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so they are not the same card). There are 12 cards considered face cards. There are 4 cards with the value 10. Let X be the number of face cards in your hand. Let Y be the number of 10's in your hand. Explain why X and Y are dependent.

A five-card poker hand dealt from a standard 52-card deck of playing cards is called a...

A five-card poker hand dealt from a standard 52-card deck of playing cards is called a three-of-a-kind hand if it contains exactly three cards of the same rank (e.g. 3 aces and 2 other cards). How many distinct three-of-a-kind hands can be dealt with? Calculate a numeric answer.

Assume that 5 cards are dealt at random from a standard deck of 52 cards (there...

Assume that 5 cards are dealt at random from a standard deck of 52 cards (there are 4 suits in the deck and 13 different values (ranks) per each suit). We refer to these 5 cards as a hand in the rest of this problem. Calculate the probability of each of the following events when dealing a 5-card hand at random. (a) Exactly one pair: This occurs when the cards have numeric values a, a, b, c, d, where a,...

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1. Five cards are dealt at random from a well-shuffled deck of 52 playing cards. Find...

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