Question

An urn contains seven balls, numbered from 1 to 7. Two balls are drawn out randomly, with an equal likelihood for each outcome.

(a) What is the probability that the sum of the numbers is greater than 10?

(b) What is the probability that the product is odd?

(c) What is the probability that the sum is greater than 10 and the product is odd?

(d) What is the probability that the sum is greater than 10 or the product is odd?

Answer #1

A bowl contains four balls numbered 1,2,3,4. If two balls are
randomly drawn from the bowl, without replacment , and the random
variable X is the sum of the numbers on the two balls drawn.
a) Find the probabiltiy density function.
b) Find P(x>3)
c) Determine the expected value and the standard deviation.

Suppose that a ball is selected at random from an urn with balls
numbered from 1 to 100, and without replacing that ball in the urn,
a second ball is selected at random. What is the probability
that:
1. The sum of two balls is below five.
2. Both balls have odd numbers.
3. Two consecutive numbers ar chosen, in ascending order

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.

A jar contains five red balls numbered 1 to 5, and seven green
balls numbered 1 to 7. A ball is drawn at random from the jar. Find
the following conditional probabilities. (Enter your probabilities
as fractions.)
(a) The ball is red, given that it is numbered 1. - answer
1/2
(b) The ball is green, given that it is numbered 7. - answer
1
Don't know the answer for:
(c) The ball is red, given that it has an...

Five balls numbered 1,2,3,4, and 5 are placed in an urn. Two
balls are randomly selected from the five, and their numbers noted.
Let Y be the greater of the two sampled numbers.
a) Find the pdf of Y
b) Find E(Y) and Var(Y)

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...

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.]

A box contains 80 balls numbered from 1 to 80. If 15 balls are
drawn with replacement, what is the probability that at least two
of them have the same number?

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.

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

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