Question
In: Statistics and Probability
An urn contains red and green colored balls. You draw a sample of five balls from...
An urn contains red and green colored balls. You draw a sample of five balls from the urn.
(a) Suppose the urn contains 18 balls, half of which are red. What is the probability that the sample contains a red ball?
(b) Suppose the urn contains 144 balls, half of which are red. What is the probability that the sample contains a red ball?
(c) Suppose the urn contains 144 balls, 10 of which are red. What is the probability that the sample contains a red ball?
Solutions
orchestra answered 2 years agoRelated Solutions
An urn contains colored balls;5 red balls, 8 green balls, and 10 blue balls. Suppose ...
An urn contains colored balls;5 red balls, 8 green balls, and 10
blue balls. Suppose If the 3 balls are drawn one after another
without replacement, what is the probability that the colors
observed will be Red, Green, Blue in this order? If the three
balls are drawn simultaneously from the urn (without replacement),
what is the probability that the selected balls will be all
different?
An urn contains 4 green balls, five blue balls, and seven red balls. You remove five...
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
An urn contains 6 red balls and 4 green balls. A sample of 7 balls is...
An urn contains 6 red balls and 4 green balls. A sample of 7
balls is selected at random.
a. How many different samples are possible?
b. How many samples contain 5 red and 2 green balls?
c. How many sample contain all red balls?
d. How many samples contain at least 4 red balls?
e. What is the probability in a draw of 7 balls there is 3 red
and 4 green?
Urn 1 contains 8 green balls and 10 red balls. Urn 2 contains 7 green balls...
Urn 1 contains 8 green balls and 10 red balls. Urn 2 contains 7
green balls and 5 red balls. A die is rolled, if a 1 or 2 is
rolled, a ball is chosen from urn 1, if a 3, 4, 5, or 6 is rolled,
a balls is chosen from urn 2. What is the probability of selecting
a green ball? Please show all work.
Urn A contains 5 green and 4 red balls, and Urn B contains 3 green and...
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.
Urn A contains 5 green and 4 red balls, and Urn B contains 3 green and...
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 five red balls, six white balls, and seven blue balls, and a sample...
An urn contains five red balls, six white balls, and seven blue
balls, and a sample of five balls is drawn at random without
replacement.
(a) What is the size of the sample space?
(b) Compute the probability that the sample contains three red
balls, one white ball and one blue ball.
(c) Compute the probability that the sample contains at least
one ball of each color.
(d) Compute the probability that all of the balls in the sample
are...
An urn contains 6 red balls and 4 green balls. Three balls are chosen randomly from...
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 5 green balls and 8 red balls. One of the balls is drawn...
An urn contains 5 green balls and 8 red balls. One of the
balls is drawn at random.
The drawn ball is returned to the urn with 3 additional balls
of the same color. A second
ball is drawn from the newly constituted urn.
a. What is the probability the second ball is green?
b. Given that the second ball was red, what is the probability
that the first ball was green?
An urn contains 10 red balls and 5 green balls. Balls are randomly selected, one at...
An urn contains 10 red balls and 5 green balls. Balls are
randomly selected, one at a time, with replacement, until a red one
is obtained. What is the probability that exactly k draws are
needed? What is the probability that at least k draws are needed?
Define a random variable associated with this experiment. Determine
its probability mass function and cumulative distribution function,
sketch their graphs. Find the expectation, variance and standard
deviation of X.
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