3 red balls, 4 blue balls, and 3 green balls are randomly placed
in a line....
3 red balls, 4 blue balls, and 3 green balls are randomly placed
in a line. What is the probability that there is at least one red
and at least one blue between each pair of green balls?
An urn contains 4 red balls and 3 green balls. Two balls are
sampled randomly.
Let W denote the number of green balls in the sample when the
draws are done with replacement. Give the possible values and the
PMF of W.
A box contains 8 red balls, 4 green balls, and 3 blue balls. You
pull 2 balls from the box (one at a time) WITHOUT
replacement.
**LEAVE ALL ANSWERS AS FRACTIONS**
Find the probability of the following:
a.) P(Red on 1st ball AND Red on 2nd ball) =
b.) P(Green on 1st ball AND Red on 2nd ball)
=
c.) P(Blue on 1st ball AND Green on 2nd ball)
=
d.) What is the probability of drawing 2 green
balls...
An urn contains 7 red and 10 blue balls. If 4 balls are to be
randomly selected without replacement, what is the probability that
the first 2 selected are red and the last 2 selected are blue?
Explain each step ?
A bag contains 4 Blue, 5 red and 3 green balls. Debolina is
asked to pick up three balls at random, one by one without
replacement from that bag. If the balls picked up are of same
colour then Debolina will get Rs. 7000, if the balls picked up are
of different colour, then she will get Rs. 9000, but otherwise she
has to pay Rs. 4000.
a) Find the expected gain of Debolina if she plays the game.
b)...
An urn contains 6 red balls and 4 green balls. Three balls are
chosen randomly from the urn, without replacement.
(a) What is the probability that all three balls are red? (Round
your answer to four decimal places.)
(b) Suppose that you win $20 for each red ball drawn and you
lose $10 for each green ball drawn. Compute the expected value of
your winnings.
An urn contains 4 green balls, five blue balls, and seven red
balls. You remove five balls at random without replacement. Let X
be the random variable that counts the number of green balls in
your sample. a) Find the probability mass function p(x) describing
the distribution of X. b) Find the mean and variance of X
3. An urn contains 12 red balls and 8 green balls. Six balls are
drawn randomly with replacement
a. Find the probability of drawing exactly two red balls?
b. Find the probability of drawing at least one green ball?
c. Find the probability of drawing exactly two green balls when
the drawings are done without replacement?
There are three types of balls in a box: 5 red, 3 blue and 2
green. You draw 3 balls at once (without replacement) from this box
and record: Y1=the # of red balls, Y2=the # of blue balls that you
drew. Find the joint probability distribution of Y1, Y2, by first
writing the possible values for y1, y2 in rows and columns and then
filling in the probabilities within this table. Then check that the
sum of the entries...
A box contains 4 red balls, 3 yellow balls, and 3 green balls.
You will reach into the box and blindly select a ball, take it out,
and then place it to one side. You will then repeat the experiment,
without putting the first ball back. Calculate the probability that
the two balls you selected include a yellow one and a green
one.
3. Consider a binomially distributed random variable constructed
from a series of 8 trials with a 60%...
13. A bin contains 3 red and 4 green balls. 3 balls are chosen
at random, with replacement. Let the random variable X be the
number of green balls chosen. a. Explain why X is a binomial random
variable. b. Construct a probability distribution table for X. c.
Find the mean (expected value) of X. d. Use the law of Large
Numbers to interpret the meaning of the expected value of X in the
context of this problem.