Question

Suppose a bowl has 5 chips; two chips are labeled "2", and three chips are labeled "3".

Suppose two chips are selected at random WITHOUT replacement. Let the random variable X

equal the product of the two draws (e.g. if the first draw is a 2 and the second draw

is a 3, then the product is 2 x 3 = 6).

Answer #1

Let a bowl contain 30 chips of the same size and shape. Only
one of those chips is red. Continue to draw chips from the bowl,
one at a time at random and without replacement, until the red chip
is drawn.
(a) Find the p.m.f. of X, the number of trials needed to draw
the red chip. Show your work.
(b) Compute the mean and variance of X. Show your work.
(c) Determine P( X less than or equal to...

Five identical bowls are labeled 1, 2, 3, 4, and 5. Bowl
i contains i white and 5 − i black
balls, with i = 1, 2, , 5.
A bowl is randomly selected and two balls are randomly selected
(without replacement) from the contents of the bowl.
Given that both balls selected are white, what is the
probability that bowl 5 was selected?

Suppose that in an assortment of 25 calculators there are 5 with
defective switches. Draw with and without replacement. (Enter the
probabilities as fractions.)
(a) If one machine is selected at random, what is the
probability it has a defective switch? with replacement _____
without replacement ____
(b) If two machines are selected at random, what is the
probability that both have defective switches? with replacement ___
without replacement ____
(c) If three machines are selected at random, what is...

Three random draws with replacement will be made from a box
containing 5 tickets labeled:
1, 2, 2,
3, 3.
The probability that a ticket labeled 2 will be
drawn at least once is _____ out of 125.

A lot of 106 semiconductor chips contains 29 that are defective.
Round your answers to four decimal places (e.g.
98.7654).
a) Two are selected, at random, without replacement, from the
lot. Determine the probability that the second chip selected is
defective.
b) Three are selected, at random, without replacement, from the
lot. Determine the probability that all are defective.

A lot of 101 semiconductor chips contains 25 that are
defective.
(a)
Two are selected, one at a time and without replacement from
the lot. Determine the probability that the second one is
defective.
(b)
Three are selected, one at a time and without replacement. Find
the probability that the first one is defective and the third one
is not defective.

a. Consider 5 fish in a bowl: 3 of them are
red, and 1 is green, and 1 is blue. Select the fish one at a time,
without replacement, until the bowl is empty. Let X=1 if all of the
red fish are selected, before the green fish is selected; and X=0
otherwise. Find E(X). (Hint: You already found pX(1) on Monday, and
pX(0) is just the complementary probability.)
b. Suppose that 60% of people in Chicago are
fans of...

A dresser contains 4 yellow socks and 5 blue socks. Draw three
socks with replacement. Let X be the number of yellow socks on the
first two draws, and Y the number of yellow socks on the last two
draws. Make a table showing the joint distribution of X and Y .
Compute the expected number of yellow socks on the first two
draws.

1. Suppose that a bag contains 3 red chips and 7 white chips.
Suppose that chips are drawn from the bag with replacement, i.e.
the chips are returned to the bag and shuffled before the next chip
is selected. Identify the correct statement.
a.
If many chips are selected then, in the long run, approximately
30% will be red.
b.
If ten chips are selected then three will definitely be red.
c.
If seven consecutive white chips are selected then...

Two numbers are selected at random and with replacement from the
set {1, 2, 3, 4, 5, 6}.
What is the probability that the first one is equal to the
second?
What is the probability that the first one is greater than the
second?

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