Question

Suppose
you are picking one number from the set of natural numbers from 97
to 4. What is the minimum number of picks to guarantee that you
will have picked one number at least 3 times?

Answer #1

Combinatorics
A prize draw allows you to enter by picking 3 numbers from { 1 ,
2 ,..., 14 } . You will win a prize if you choose two of the three
numbers that they will draw.
a) Show that it is possible to guarantee a win by having 14
entries in the draw.
b) Explain whether or not a similar strategy would work if the
numbers were chosen from { 1 , 2 ,..., 21 }

Alice, Bob, and Charlie each pick random numbers from the set
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10} independently.
(a) What is the probability that Alice and Bob pick the same
number?
(b) What is the probability that Alice, Bob, and Charlie all
pick even numbers?
(c) What is the probability Alice’s pick is at most 4 (including
4) OR Bob’s pick is at least 8?
(d) Given that Alice picks 8, what is the probability that...

What is the
probability of picking 6 numbers out of 44 numbers and
getting…..
a)
6 out of 6
correct?
b)
5 out of 6
correct?
c)
4 out of 6
correct?
d)
3 out of 6
correct
plesse show
your work and give full explaination how did you get
it.
and give
answer in number

In the Powerball® lottery, the player chooses five numbers from
a set of 69 numbers without replacement and one “Powerball” number
from a set 26 numbers. The five regular numbers are always
displayed and read off in ascending order, so order does not
matter. A player wins the jackpot if all six of the player’s
numbers match the six winning numbers.
a. How many different possible ways are there to select the six
numbers?
b. How many tickets would someone...

A number is randomly selected from the set of numbers that are
less than 15. What is the probability that the number chosen is
divisible by 4 or less than 6?

Two numbers are selected at random and with replacement from the
set {1, 2, 3, 4, 5, 6}.
What is the probability that the first one is equal to the
second?
What is the probability that the first one is greater than the
second?

In a lottery 5 numbers and chosen from the set {1,...,90}
without replacement. We order the five numbers in increasing order
and we denote by X the number of times the difference between two
neighboring numbers is 1. (E.g. for {1,2,3,4,5} we have X=4, for
{3,6,8,9,24} we have X=1, and for {12,14,43,75,88} we have X=1. )
Find EX.

Pigeonhole Principle:
What is the minimum number of students that must be assigned to
a classroom with 14 tables to guarantee that some table will have
at least 3 students?
Suppose a set of 8 numbers are selected from the set {1, 2, 3,
..., 13, 14}. Show that two of the selected numbers must sum to 15.
(Hint: think about how many subsets of 2 elements you can form such
that the sum of the values of the two...

2. Suppose you have
a data set of 7 numbers. If the constant 5 is added to each value
in the set, what happens to the mean? What happens to the standard
deviation?
3. There is a chowder eating contest in a small New England
town. The distribution of the amount of chowder consumed is
bell-shaped with mean 32 ounces and variance 64 ounces. If two
hundred people participated in the contest, find the following.
a. The number of people...

If you roll a die, you get one of the following numbers: 1, 2,
3, 4, 5, 6. Each possibility occurs with equal probability of 1/6.
The expected value of a dice roll is E(D)= 3.5 and the variance of
a dice roll is Var(X) = 2.917.
a) Suppose you roll a die and then add 1 to the roll to get a
new random variable taking one of the following numbers:
2,3,4,5,6,7. What is the variance of this new...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 34 minutes ago

asked 34 minutes ago

asked 35 minutes ago

asked 43 minutes ago

asked 43 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago