Question 6: In this question we will explore some of the weirdness of conditional probability (it's not actually that weird once we understand it, but it can seem very weird). Texas Hold'em is a variety of poker where each player is dealt 2 cards initially. Five other cards are dealt to the middle for all players to share, however for this exercise we will focus on the first 2 cards you are dealt. Assume the dealer is using a single deck of 52 cards. a) What is the probability that you are dealt a pair on your first two cards? That is, two cards of the same rank. b) Your lucky number is 7, so you are keeping track of what sort of hand you get when one of your first two cards is a 7. What is the probability that you are dealt a pair on your first two cards when at least one of those two cards is a 7? How does this compare to your probability of getting a pair above? c) What is the probability of getting a pair when there are no 7's in your hand? How does this compare to the probabilities above? d) There is something weird about 7's. You dig a little deeper. You keep track of the outcomes when one of the first two cards you are dealt is the 70. Given that you've been dealt two cards and one of those cards is the 7◊, what is the probability that you've been dealt a pair (that is, that your other card is also a 7)? e) What is the probability that you have a pair given that you have at least one 7 or at least one 8 in your hand? Is this higher or lower than the probability of having a pair given that you have at least one 7 in your hand (part b))? f) As a bonus, try and explain the different probabilities for parts a) through e) given that they all deal with the probabilities of getting a pair.
Question 6: In this question we will explore some of the weirdness of conditional probability (it's not actually that weird once we understand it, but it can seem very weird). Texas Hold'em is a variety of poker where each player is dealt 2 cards initially. Five other cards are dealt to the middle for all players to share, however for this exercise we will focus on the first 2 cards you are dealt. Assume the dealer is using a single deck of 52 cards. a) What is the probability that you are dealt a pair on your first two cards? That is, two cards of the same rank. b) Your lucky number is 7, so you are keeping track of what sort of hand you get when one of your first two cards is a 7. What is the probability that you are dealt a pair on your first two cards when at least one of those two cards is a 7? How does this compare to your probability of getting a pair above? c) What is the probability of getting a pair when there are no 7's in your hand? How does this compare to the probabilities above? d) There is something weird about 7's. You dig a little deeper. You keep track of the outcomes when one of the first two cards you are dealt is the 70. Given that you've been dealt two cards and one of those cards is the 7◊, what is the probability that you've been dealt a pair (that is, that your other card is also a 7)? e) What is the probability that you have a pair given that you have at least one 7 or at least one 8 in your hand? Is this higher or lower than the probability of having a pair given that you have at least one 7 in your hand (part b))? f) As a bonus, try and explain the different probabilities for parts a) through e) given that they all deal with the probabilities of getting a pair.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
Related questions
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answer all parts: a), b), c), d), e), f)
Transcribed Image Text:Question 6:
In this question we will explore some of the weirdness of conditional probability (it's not
actually that weird once we understand it, but it can seem very weird). Texas Hold 'em is
a variety of poker where each player is dealt 2 cards initially. Five other cards are dealt to
the middle for all players to share, however for this exercise we will focus on the first 2 cards
you are dealt. Assume the dealer is using a single deck of 52 cards.
a) What is the probability that you are dealt a pair on your first two cards? That is, two
cards of the same rank.
b) Your lucky number is 7, so you are keeping track of what sort of hand you get when
one of your first two cards is a 7. What is the probability that you are dealt a pair
on your first two cards when at least one of those two cards is a 7? How does this
compare to your probability of getting a pair above?
c) What is the probability of getting a pair when there are no 7's in your hand? How
does this compare to the probabilities above?
d) There is something weird about 7's. You dig a little deeper. You keep track of the
outcomes when one of the first two cards you are dealt is the 7◊. Given that you've
been dealt two cards and one of those cards is the 7◊, what is the probability that
you've been dealt a pair (that is, that your other card is also a 7)?
What is the probability that you have a pair given that you have at least one 7 or at
least one 8 in your hand? Is this higher or lower than the probability of having a pair
given that you have at least one 7 in your hand (part b))?
f) As a bonus, try and explain the different probabilities for parts a) through e) given
that they all deal with the probabilities of getting a pair.
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