Question

We have two urns: Urn A contains 6 red balls and 4 white balls,
Urn B contains 4 red balls and 8 white balls. A die is rolled, if a
number less than 3 appears; we go to box A; if the result is 3 or
more, we go to ballot box B. Then we extract a ball. It is
requested:

to. Probability that the ball is red and ballot box B.

b. Probability that the ball is white.

Answer #1

Suppose that an urn contains 8 red balls and 4
white balls. We draw 2 balls
from the urn without replacement.
Now suppose that the balls have
different weights, with each red ball having weight
r and each white ball having weight w. Suppose that the
probability that a given ball in
the urn is the next one selected is its weight divided by the
sum of the weights of all
balls currently in the urn.
Now what is the...

One urn contains 10 red balls and 10 white balls, a second urn
contains 8 red balls and 4 white balls, and a third urn contains 5
red balls and 10 white balls. An urn is selected at random, and a
ball is chosen from the urn. If the chosen ball is white, what is
the probability that it came from the third urn? Justify your
answer.

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...

An urn contains 3 white balls and 7 red balls. A second urn
contains 7 white balls and 3 red balls. An urn is selected, and the
probability of selecting the first urn is 0.2. A ball is drawn from
the selected urn and replaced. Then another ball is drawn and
replaced from the same urn. If both balls are white, what are the
following probabilities? (Round your answers to three decimal
places.)
(a) the probability that the urn selected...

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.

Given 3 urns, one contains 2 black balls, the second contains 2
white balls, and the third contains 1 ball of each color. An
urn is chosen at random and a ball is drawn from it -- the ball is
white. What is the probability that the other ball in that urn is
also white?

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...

Urn A has 17 white and 4 red balls. Urn B has 9 white and 13 red
balls. We flip a fair coin. If the outcome is heads, then a ball
from urn A is selected, whereas if the outcome is tails, then a
ball from urn B is selected. Suppose that a red ball is selected.
What is the probability that the coin landed heads? n

An urn has 15 white balls, 13 green balls, 10 yellow balls, and
12 red balls. Determine the probability that it will come
out:
a. A red ball
b. A green ball
c. A white ball
d. A red ball and a yellow ball
e. A ball that is not green
Calculate the probability that the number 89 will come out when
taking a ball from a bag with 120 balls numbered from 1 to 120.
Calculate the probability that...

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