Question

An urn has 6 balls that are identical except that 3 are white and 3 are red. A sample of 4 is selected randomly without replacement. A) What is the probability that exactly 2 are white and 2 are red? B) What is the probability that at least 2 of the balls are white?

Answer #1

We can convert this problem in to binomial distribution

Probability of selecting white ball is

Let

Number balls selected ( which is same as a sample of 4 is selected randomly without replacement )

A) The probability that exactly 2 are white and 2 are red is

B) The probability that at least 2 of the balls are white is

An urn has 9 balls that are identical except that 6 are white
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replacement.
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What is the probability that at least 5 of the balls are
white?

An urn has 16 balls that are identical except that 8 are white
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What is the probability that exactly 7 are white and 2 are
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What is the probability that at least 7 of the balls are
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an urn has 22 balls that are identical except that 7 are
white, 8 are red, and 7 are blue. what is the probability that all
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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 has 6 red and 4 white balls. Two balls are chosen at
random and without replacement.
Let Y be the number of red balls among those selected.
a. Find the probability function (pmf) of Y.
b. Find the moment-generating function of Y.

Suppose you have an urn with 20 balls including 10 red, 6 white
and 4 black. We randomly select 5 balls with replacement. What is
the probability that at least one of the 5 selected balls is red
?
Select one:
a. 0.031250 b. 0.968750 c. 0.000320 d. 0.500000 e. 0.999680

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?

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...

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...

An urn contains 10 numbered balls, of which 6 are red and 4 are
white. A sample of 4 balls is to be selected.
*How many samples contain at least 3 red balls?

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