Question

From an urn containing 9 red balls and 6 green balls, 4 balls are taken without replacement. Determine the probability that all 4 ball are green

Give the probability if the same experiment is preformed with replacement and the same outcome is obtained

Answer #1

Two balls are chosen randomly from an urn containing 6 red and 4
black balls, without replacement. Suppose that we win $2 for each
black ball selected and we lose $1 for each red ball selected. Let
X denote the amount on money we won or lost.
(a) Find the probability mass function of X, i.e., ﬁnd P(X = k) for
all possible values of k.
(b) Compute E[X].
(c) Compute Var(X)

Urn A contains 6 green and 4 red balls, and Urn B contains 3
green and 7 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
A. Let X = the number of green balls in Urn A after this process.
List the possible values for X and then find the entire probability
distribution for X.

2. Urn A contains 6 green and 4 red balls, and Urn B contains 3
green and 7 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
A. Let X = the number of green balls in Urn A after this process.
List the possible values for X and then find the entire probability
distribution for X.

Urn A has 8 Red balls and 5 Green balls while Urn B has 1 Red
ball and 3 Green balls.
A fair die is tossed. If a “5” or a “6” are rolled, a ball is drawn
from Urn A. Otherwise, a ball is drawn from Urn B.
(a) Determine the conditional probability that the chosen ball is
Red given that Urn A is selected?
(b) Determine the conditional probability that the chosen ball is
Red and Urn B...

We have three urns: the first urn has 6 red balls and 4 green
balls; the second urn has 15 red balls and 5 green balls and the
third urn has 20 red balls and 10 green balls. We pick 4 balls from
the first urn (sampling with replacement); we select 5 balls from
the second urn (sampling with replacement) and we select 10 balls
from the third urn (sampling with replacement). Let X1 denote the
number of red balls...

For an urn containing 4 red balls and 6 green balls, let the
number of balls randomly drawn be the number of heads turning up
when 5 fair coins have been previously flipped. What is the
probability of drawing 3 green balls?
why do we need binomial theorem for this

Urn A contains 5 green and 4 red balls, and Urn B contains 3
green and 6 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
A. Let X = the number of green balls in Urn A after this process.
List the possible values for X and then find the entire probability
distribution for X.

An urn contains 1 white, 2 black, 3 red, and 4 green balls. If 6
balls are selected randomly (without replacement) and X represents
the number of selections that are either red or green, find: (a)
the probability mass function for X. (b) the expected value of X
(calculate this value directly by using the probability mass
function from part a).

An urn contains 4 red balls and 3 green balls. Two balls are
sampled randomly.
Let Z denote the number of green balls in the sample when the
draws are done without replacement. Give the possible value of Z
and its probability mass function (PMF).

A bag contains 4 red balls and 5 green balls. If 4 balls are
taken from the bag without replacement, find the probability
that
i) 2 red balls and 2 green balls are chosen
ii) the first two balls are red and the second two balls are
green
iii) the colors of the four balls alternate

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