Question

David draws with replacement from a bag containing 1 red and 2 black balls.

(a) If David draws 5 balls total what is the expected number of red balls drawn?

(b) If David draws 5 balls total what is the variance of the number of red balls drawn?

(c) If N is the number of draws until David has selected 200 black balls, compute E [N].

Answer #1

Two balls are drawn in succession without replacement from a bag
containing
2 red balls, 1 green balls and 3 green balls. Let X and Y denote
the number
of red and green balls respectively. Find
a) f(x,y) the expression for the joint p.d.f of X and Y [5
Marks]
b) f(x) the expression for the marginal pdf of X [5 Marks]
c) f(y) the expression for the marginal pdf of Y [5 Marks]
d) f(y/x), the expression for the...

1. Two balls are drawn from a bag containing 9 white balls and 2
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drawn, what is the probability that the following will occur?
(Enter your probabilities as fractions.) (a) both balls are red (b)
both balls are white (c) the first ball is red and the second is
white (d) one of the balls is black
2.The table gives the results of a survey of 1000 people...

Two balls are drawn from a bag containing 5 white balls and 7
red balls. If the first ball is replaced before the second is
drawn, what is the probability that the following will occur?
(Enter your probabilities as fractions.)
(a) both balls are red
(b) both balls are white
(c) the first ball is red and the second is white
(d) one of the balls is black

Urn A has 1 red and 2 black balls. Urn B has 2 red and 1 black
ball. It is common knowledge that nature chooses both urns with
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balls is drawn with replacement from one of the urns. Experimental
subjects do not know which urn the balls are drawn from. Let x
denote the number of red balls that come up in the sample of 6
balls, x=0,1,2,...,6. Suppose that...

Two balls are chosen randomly from an urn containing 6 red and 4
black balls, without replacement. Suppose that we win $2 for each
black ball selected and we lose $1 for each red ball selected. Let
X denote the amount on money we won or lost.
(a) Find the probability mass function of X, i.e., ﬁnd P(X = k) for
all possible values of k.
(b) Compute E[X].
(c) Compute Var(X)

Now we have a magical urn which has N > 0 black balls and M
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one is drawn. Compute the expected number of balls drawn.

Two balls are drawn from a bag containing 4 white balls and 3
red balls. If the first ball is replaced before the second is
drawn, what is the probability that the following will occur?
(Enter your probabilities as fractions.)
(a) both balls are red
(b) both balls are white
(c) the first ball is red and the second is white
(d) one of the balls is black
A die is thrown twice. What is the probability that a 2...

6. A jar contains 5 red balls and 5 black balls. Two balls are
successively drawn from the jar. After the first draw the color of
the ball is noted, and then the selected ball is returned to the
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with another black ball; if black ball is drawn it is returned to
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One ball is chosen at random from a bag containing 12 red balls,
3 yellow balls, and 5 green balls.
i. If 1000 trials are completed (with replacement), about how
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ii. If two balls are selected at random without replacement,
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are drawn without replacement, what is the probability that no
black balls are drawn? Express your answer as a fraction or a
decimal number rounded to four decimal places.

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