Question

There are n people in a room. Each of them takes their shoes off and puts them in a large urn. if each person then selects two individual random shoes without replacement from the urn, what's the probability everyone has their own shoes?

Answer #1

Suppose that 116 people throw their hats in a box and
then each picks one hat at random. Each hat can be picked by only
one person, and each assignment of hats to persons is equally
likely.
Let and be two random
variables. takes the value 856 if the th person selects
his/her own hat, and takes the value 0 otherwise.
Similarly, takes the value 856 if the th person selects
his/her own hat, and takes the value 0 otherwise. Note
that ( is not...

Suppose that 84 people throw their hats in a box and
then each picks one hat at random. Each hat can be picked by only
one person, and each assignment of hats to persons is equally
likely.
Let and be two random
variables. takes the value 521 if the th person selects
his/her own hat, and takes the value 0 otherwise.
Similarly, takes the value 521 if the th person selects
his/her own hat, and takes the value 0 otherwise. Note
that ( is not...

If there are N people in a room,
What is the probability that at least two of them share the same
birthday (the same
day of the same month) a year = 365 days?
How many people are needed such that the probability is better
than even?

Suppose there are n ≥ 2 people in a room, each of whom owns a
hat. Suppose the n hats are collected and then randomly assigned to
the people. Find the expected value and variance of the number of
people who get their own hat.

There are “n” candies
in a jar. 7 of the candies are red. The rest of the candies are
blue. Kevin takes at random a candy from the jar.
He eats the candy
(clue: is this a "replacement" or "without replacement"
problem?). Kevin then takes at random another candy from the jar
(clue: this second candy is picked from how many total candies?
less or equal to "n"?) . He eats the candy. The probability that
Kevin eats 2 red...

A large company with n employees has a scheme according to which
each employee buys a Christmas gift and the gifts are then
distributed at random to the employees. What is the probability
that someone gets his or her own gift?

I write each of the letters ‘L’, ‘I’, ‘O’, ‘N’ on separate
pieces of paper and put these into a hat. I close my eyes and begin
picking the pieces of paper from the hat and reading off the
letters written on the pieces of paper. a. If I pick 3 pieces of
paper without replacement, then what is the probability that the
letters can be rearranged to spell ‘OIL’? b. If I pick pieces of
paper with replacement until...

Discrete Math:
The Birthday Problem investigates the minimum number of people
needed to have better than a 50% chance of at least two people have
the same birthday. Calculating this probability shows that n = 23
yields a probability of approximately .506. Use the probabilistic
algorithm called the Monte Carlo algorithm and find the number of
people in a room that yields an approximate probability greater
than .75.
Please use the following list to complete the problem
● Adopt the...

Each of n people are randomly and independently assigned a
number from the set {1, 2, 3, . . . , 365} according to the uniform
distribution. We will call this number their birthday. (a) What is
the probability that no two people share a birthday? (b) Use a
computer or calculator to evaluate your answer as a decimal for n =
22 and n = 23.

Suppose 83 percent of all people in a sample support global
warming, if 74 percent of the people surveyed are women , and 60
percent fit both categories. What is the chance of selecting a
person randomly who has neither attributes?
a.0.03b.0.39c.0.24d.0.09 Are the two attributes Independent of each
other? a.The attributes are Independent because the product of the
probability of the two happening simultaneously is equal to the
product of the individual probabilities. b.The attributes are not
Independent because...

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