Discrete Math Q Given a randomly picked five-card poker hand, What is the probab
ID: 3123269 • Letter: D
Question
Discrete Math
Q Given a randomly picked five-card poker hand,
What is the probability that the five-card poker hand contains the Ace of Diamond?
What is the probability that the five-card poker hand contains the Jack of Spade, Queen of Club and King of Heart?
What is the probability that the five-card poker hand contains a flush (five cards of the same suits)?
Q Given a group of 13 students,
You want to pick 5 students to stand in a row for a picture, how many different arrangements are there?
You want to pick three students to form a committee, how many different selections are there?
What can you say about the birth dates (birth days or months) of those students based on the pigeonhole principle?
Q When you roll two dice,
How many possible outcomes do you have in total?
What is the probability that the two dice sum up to 9?
What is the probability that the two dice come up with different values?
How many bit strings with length 10 that starts either with 10 or 01?
How many bit-strings with length 10 that either starts with 11 or ends with 00?
How many bit-strings with length 10 that has exactly three 1s?
How many bit-strings with length 10 that has at most three 1s?
Q Consider the permutations of the letters A, B, C, D, E, F, G, H.
How many permutations are there in total?
How many permutations contain ABC?
How many permutations contain AG, ED, and BCH?
Q Let f(x) = 2x be the function that maps the set of integers to the set of integers.
Is f one-to-one?
Is f onto?
Let g(x) = x 3 be the function that maps the set of real numbers to the set of real numbers.
Is g one-to-one?
Is g onto?
Explanation / Answer
What is the probability that the five-card poker hand contains the Ace of Diamond?
Ans: P(getting the ace of diamond in 5 cards)
= P(1st is AD or 2nd is AD or 3rd is AD or ... or 5th is AD)
Since these event are mutually exclusive (getting one excludes the others from happening), then you can just add the probabilities.
= P(1st is AD) + P(2nd is AD) + ... + P(5th is AD)
= 1/52 + 1/52 + ... + 1/52 (note that these are unconditional probabilities, so all are 1/52)
= 5/52
= 0.096153846
Given a group of 13 students,
You want to pick 5 students to stand in a row for a picture, how many different arrangements are there?
Ans Select 5 from 13 and arrange them
13C5 * 5! = 1287 * 120 = 154440
You want to pick three students to form a committee, how many different selections are there?
Ans: Select 3 from 13
13C3 = 286
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