2) Suppose that 5 cards are dealt from a shuffled standard deck. Assuming that the sample...

2) Suppose that 5 cards are dealt from a shuffled standard deck. Assuming that the sample space is uniform what is the probability of getting a straight flush?

3) Suppose that my easter egg Ameraucana (‘Zinny’) lays eggs that are brown, green, or blue with probabilities 1/2, 1/3, and 1/6 respectively. Determine the following probabilities for a dozen eggs.

(a) There are no brown eggs.

(b) All the eggs are green.

(c) There are at most 4 brown eggs.

Expert Solution

orchestra answered 2 years ago

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 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

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,...

Suppose you are dealt 5 random cards from a standard deck of 52 cards, where all...

Suppose you are dealt 5 random cards from a standard deck of 52 cards, where all cards are equally likely to appear. (a) What is your outcome space? (b) What is the probability that you receive the ace of hearts? (c) Let AH be the event that you receive the ace of hearts, AC the event that you receive the ace of clubs, AD the event that you receive the ace of diamonds, and AS the event that you receive...

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. 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

From shuffled deck of cards, 4 cards are randomly selected without replacement from shuffled deck of...

From shuffled deck of cards, 4 cards are randomly selected without replacement from shuffled deck of 52 cards. What is the probability to get at least one ace?

Consider a well shuffled deck of cards, from which 5 cards are drawn. a. Find the...

Consider a well shuffled deck of cards, from which 5 cards are drawn. a. Find the probability that you get three cards of hearts, and two cards of spades. b. Find the probability that you get three cards of the same suit, and two cards with the same suit (but different than the one of the three other cards).

draw 20 cards without replacement from a shuffled, standard deck of 52 cards. What is the...

draw 20 cards without replacement from a shuffled, standard deck of 52 cards. What is the conditional probability P (12th card and 20th card is a heart 3rd card is a club)

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...

Question