Question

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 probability that both balls are red?

Answer #1

An urn contains 8 balls, 3 white, 3 green and 2 red.
a) We draw 3 balls without replacement. Find
the probability that we don't see all three colors.
b) We draw 3 balls with replacement. Find the
probability that we don't see all three colors.

An urn contains 7 balls: 2 white, 3 green, and 2 red.
We draw 3 balls without replacement. Find the probability that
we don’t see all three colors.Probability =
We draw 3 balls with replacement. Find the probability that we
don’t see all three colors.Probability =

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.

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...

An urn has 12 balls. 8 are white balls and 4 are black
balls.
If we draw a sample of 3 balls (i.e., picking without
replacement) and given that the first two balls selected were a
black ball and a white ball, what is the conditional probability of
the third ball drawn being white?

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.

Suppose that:
Urn U1 contains 3 blue balls and six red balls, and
Urn U2 contains 5 blue ball and 4 red balls
Suppose we draw one ball at random from each urn. If the two
balls drawn have different colors, what is the probability that the
blue ball came from urn U1?

An urn contains 8 white balls and 4 red balls. The experiment
consists of drawing 2 balls at random from the urn without
replacement.
a) What is the probability that both will be the same color?
b) Same question for part A, but with replacement.

Suppose that there is a white urn containing three white balls
and one red ball and there is a red urn containing two white balls
and four red balls. An experiment consists of selecting at random a
ball from the white urn and then (without replacing the first ball)
selecting at random a ball from the urn having the color of the
first ball. Find the probability that the second ball is red.
-please state answer in fraction-

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

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