Question

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 many times would you expect to select a red ball?

ii. If two balls are selected at random without replacement, what is the probability that they are both red? Write your answer as a decimal rounded to 3 decimal places.

Answer #1

Total number of balls in bag is n(S) = 20.

Box 1 contains 4 red balls, 5 green balls and 1 yellow ball.
Box 2 contains 3 red balls, 5 green balls and 2 yellow
balls.
Box 3 contains 2 red balls, 5 green balls and 3 yellow
balls.
Box 4 contains 1 red ball, 5 green balls and 4 yellow balls.
Which of the following variables have a binomial
distribution?
(I) Randomly select three balls from Box 1 with replacement. X =
number of red balls selected
(II) Randomly...

A box contains one yellow, two red, and three green balls. Two
balls are randomly chosen without replacement. Define the following
events:
A:{ One of the balls is yellow }
B:{ At least one ball is red }
C:{ Both balls are green }
D:{ Both balls are of the same color }
Find the following conditional probabilities:
P(B\Ac)=
P(D\B)=

A box contains one yellow, two red, and three green balls. Two
balls are randomly chosen without replacement. Define the following
events:
A: \{ One of the balls is yellow \}
B: \{ At least one ball is red \}
C: \{ Both balls are green \}
D: \{ Both balls are of the same color \}
Find the following conditional probabilities: (a) P(B|D^c)
(b) P(D|C)
(c) P(A|B)

A bag contains three balls: one red, one yellow, and one blue.
Suppose you select two balls with replacement.
Write the sample space for this procedure by listing out all
the possible outcomes that could result.
What is the probability that both balls you select are the same
color?
________
What is the probability you select at least one yellow
ball?
________

A bag contains 4 red balls and 5 green balls. If 4 balls are
taken from the bag without replacement, find the probability
that
i) 2 red balls and 2 green balls are chosen
ii) the first two balls are red and the second two balls are
green
iii) the colors of the four balls alternate

Bag 1 contains six red balls, seven blue balls, and three
green balls. Bag 2 contains eight red balls, eight blue
balls, and two green balls. Bag 3 contains two red balls,
nine blue balls, and eight green balls. Bag 4 contains
four red balls, seven blue balls, and no green balls.
Bag 1 is chosen with a probability of 0.15, bag 2 with a
probability of 0.20, bag 3 with a probability of 0.35, and
bag 4 with a...

A box contains 4 red balls, 3 yellow balls, and 3 green balls.
You will reach into the box and blindly select a ball, take it out,
and then place it to one side. You will then repeat the experiment,
without putting the first ball back. Calculate the probability that
the two balls you selected include a yellow one and a green
one.

a bag contains 10 red balls and 20 white balls. a ball is
randomly chosen and replace until a red ball is selected. calculate
the mean

I have two bags. Bag 1 contains 3 green balls, while bag 2
contains 2 green balls.
I pick one of the bags at random, and throw 5 red balls in it. Then
I shake the bag and choose
4 balls (without replacement) at random from the bag.
(a) If bag 1 is picked, what is the probability that there are
exactly 2 red balls among
the 4 chosen balls?
(b) If bag 2 is picked, what is the probability...

There are 4 balls in a bag: Red, Blue, Green and Yellow.
In how many ways you can pick k balls from the urn of n with
replacement?

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