Question

An urn contains 5 red and 9 pink balls. Four balls are randomly drawn from the urn in succession, with replace

ment. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 4 balls drawn from the urn are red? Round your answer to three decimal places.

Answer #1

Solution: There are total (5+9) = 14 balls in the urn.

Since there are 5 red balls,so the probability of drawing a red ball each time = 5/14.

Also, since the drawing is independent as it has been made with replacement, the event of of drawing a red ball in every four attempts is independent of one another.

Thus, probability of getting red ball in 1st draw and in 2nd draw and in 3rd draw and in 4th draw can be written as--

P(getting red ball in 1st draw) * P(getting red ball in 2nd
draw) * P(getting red ball in 3rd draw) * P(getting red ball in 4th
draw) = (5/14) * (5/14) * (5/14) * (5/14) = 625 / 38416 =
**0.016** ( rounded
to three decimal places)

Three balls are randomly drawn from an urn that contains four
white and nine red balls. (a) What is the probability of drawing a
red ball on the third draw? (Round your answer to 3 decimal
places.) Correct: Your answer is correct. (b) What is the
probability of drawing a red ball on the third draw given that at
least one red ball was drawn on the first two draws? (Round your
answer to 3 decimal places.]

An urn contains 4 red balls and 6 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 $50 for each red
ball drawn and you lose $25 for each green ball drawn. Compute the
expected value of your winnings.

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 1 contains 7 red balls and 3 black balls. Urn 2 contains 4
red balls and 1 black ball. Urn 3 contains 4 red balls and 3 black
balls. If an urn is selected at random and a ball is drawn, find
the probability that it will be red.
enter your answer as a decimal rounded to 3 decimal places

Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 1
red ball and 3 black balls. Urn 3 contains 3 red balls and 1 black
ball. If an urn is selected at random and a ball is drawn, find the
probability that it will be red.
Enter your answer as a fraction in simplest form or a decimal
rounded to 3 decimal places.

Urn 1 contains 4 red balls and 3 black balls. Urn 2 contains 1
red ball and 3 black balls. Urn 3 contains 4 red balls and 2
black balls. If an urn is selected at random and a ball is
drawn, find the probability that it will be red.
Enter your answer as a fraction in simplest form or a decimal
rounded to 3 decimal places.
P(red)=

In an urn, there are 20 balls of four colors: red, black, yellow
and blue. For each color, there are 5 balls and they are numbered
from 1 to 5.
1) If one ball is randomly drawn from the urn, what is the
probability that the randomly selected ball is red or blue?
2) If one ball is randomly drawn from the urn, what is the
probability that the randomly selected ball is numbered 1 or
blue?

Urn A contains 5 green and 3 red balls, and Urn B contains 2
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.

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.

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?

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