A 5-card hand is dealt from a perfectly shuffled deck. Define the events: A: the hand is a four of a kind (all four cards of one rank plus a 5th card). B: at least one of the cards in the hand is an ace Are the events A and B independent?

Kyran Hudson 2020-12-30 Answered
A 5-card hand is dealt from a perfectly shuffled deck. Define the events: A: the hand is a four of a kind (all four cards of one rank plus a 5th card). B: at least one of the cards in the hand is an ace Are the events A and B independent?
You can still ask an expert for help

Want to know more about Discrete math?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Brittany Patton
Answered 2020-12-31 Author has 100 answers

The four of a kind hand has the pattern AAAAB where A and B are from distinct kinds. The number of such hands =13C1×4C4×12C1×4C1=624 Total number of combinations of different hands =52C5=2598960 P(A=Four of a kind)=(Number of favorable outcomes)/(P(A=Four of a kind)=Number of favorable outcomesTotal number of hands)
=6242598960
=0.000240
P(None of the card is Ace)=Hand with no AceTotal number of hands
=48C5(52)C5
=17123042598960=0.6588
P(Atleast one of the card is Ace)=1P(Hands with no Ace)
=10.6588
P(B)=0.3412 The number of hands having four of a kind and Ace =1C1×4C4×1C1×4C1+12C1×4C4×1C1×4C1
=48+48
=96 Total number of combinations of different hands =52C5=2598960. P(AB)=962598960
=0.000037
P(A)P(B)=0.00024×0.3412
=0.000082 Events A and B are not independent because P(AB)P(A)P(B).

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-11-09
Use proof by Contradiction to prove that the sum of an irrational number and a rational number is irrational.
asked 2021-08-02
Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B.
a) the set of sophomores taking discrete mathematics in your school
b) the set of sophomores at your school who are not taking discrete mathematics
c) the set of students at your school who either are sophomores or are taking discrete mathematics
Use these symbols:
asked 2021-08-15
How many elements are in the set { 0, { { 0 } }?
asked 2021-08-18
Discrete Mathematics Basics
1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where (a,b)R if and only if
I) everyone who has visited Web page a has also visited Web page b.
II) there are no common links found on both Web page a and Web page b.
III) there is at least one common link on Web page a and Web page b.
asked 2022-06-01
Can't solve ( A B ) C = ( A C ) ( B C ) = A ( B C ) any help?
I have discrete math exam and i can't quite figure out one example.
( A B ) C = ( A C ) ( B C ) = A ( B C )
i tried solving it like this and i got stuck: ( A B ) C = ( A B ¯ ) C ¯ , what next ?
asked 2022-05-23
Help with using the Schroeder-Bernstein Theorem?
Corresponding Counts [3 points]
Prove that | { x R | 0 x 1 } | = | { x R | 4 < x < 7 } | .
asked 2021-08-06
Let A be the set of students in your discrete math class and B is the set of students at Arizona majoring in computer science.
A.) Describe the students in the set B\A?
b.) Which set represents the students majoring in computer science in your discrete math class?

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question