Answer:-
Given that:-
Let X be the number of spades in the spades
Total cards
(0 cards from spades & all 5 from there )
So, this is the card of a hypergeometric distribution
So, one card N=52 , n= 5, M = 13
(a) What is the probability that a 5-card poker hand has at least three
spades?
(b) What upper bound does Markov’s Theorem give for this
probability?
Markov's inequality
If x is a Hypageometric random variable and a>0,
then,
So, as
So,
(c) What upper bound does Chebyshev’s Theorem give for this probability?
Chebyshev’s inequaility:-
&
So,
So,
(because X is a positive R-V)
(a) What is the probability that a 5-card poker hand has at least three spades? (b)...
What is the probability that there are more spades than hearts in a five-card poker hand?
1. From a standard deck of 52 cards, how many 5-card poker hands are there, that have at least 3 spades? (Hint: divide the problem in cases: a poker hand has 3 spades, 4 spades, 5 spades.)
In a game of poker, what is the probability that a five-card hand will contain a four of a kind?
Poker is a card game where you are dealt a 5 card hand from a standard deck of 52 cards. This deck has 4 suits and 13 cards per suit. The rarer your hand, the higher its worth. (a) What is the probability of getting a “Full House”? A Full House is a hand where 3 cards share the same number or face, and the other 2 cards also share a different number or face. (b) What is the probability...
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2. In a game of poker, you are dealt 5 cards. What is the probability that you will be dealt the worst hand: one that contains only a "high card" (no pairs, straights, etc.)? Note: The Wikipedia page for Poker Probability gives a mathematical expression for the number of ways this can happen, but it may not be obvious why that expression is correct. Give a detailed explanation. Round to at least 3 decimal places. (5 pts)
Step 1: Doyle, a professional poker player, is at the poker table. As he sits at the table looking at his hand and at the upturned cards on the table, Doyle has seen 24 cards, and the only hearts are the 2 in his hand. None of other players have any hearts. The full deck contains 13 hearts among its 52 cards. Doyle is hoping the next three cards dealt to him will be hearts. This outcome would give him...