Question

A box contains

22

red,

22

white and

33

green balls. Two balls are drawn out of the box in succession
without replacement. What is the probability that both balls are
the same color?

Answer #1

Red = 22

White = 22

Green = 33

Total = 77

Case 1:

Both are Red

Probability of selecting 2 balls from 77 balls =

Probability of selecting 2 Red from 22 Red =

So,

P(2 Red) = 231/2926 = 0.0789

Case 2:

Both are White

Probability of selecting 2 balls from 77 balls =

Probability of selecting 2 White from 22 White =

So,

P(2 White) = 231/2926 = 0.0789

Case 3:

Both are Green

Probability of selecting 2 balls from 77 balls =

Probability of selecting 2 Green from 33 Green =

So,

P(2 Green) = 528/2926 = 0.1805

So,

P(same color) = 0.0789 + 0.0789 + 0.1805 = 0.3383

So,

Answer is:

**0.3383**

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)=

Two balls are drawn in succession out of a box containing 7 red
and 3 white balls. Find the probability that the second ball was
red, given that the first ball was: (A) replaced before the
second draw. (B) not replaced before the second draw.

A bag contains 7 red balls and 5 white balls. Two balls are
drawn without replacement. (Enter your probabilities as
fractions.)
(a) What is the probability that the second ball is white, given
that the first ball is red?
(b) What is the probability that the second ball is red, given that
the first ball is white?
(c) Answer part (a) if the first ball is replaced before the second
is drawn.

A bag contains 6 red balls and 7 white balls. Two balls are
drawn without replacement. (Enter your probabilities as
fractions.)
(a) What is the probability that the second ball is white, given
that the first ball is red?
(b) What is the probability that the second ball is red, given
that the first ball is white?
(c) Answer part (a) if the first ball is replaced before the
second is drawn.

Exercise 2 A box contains 3 white balls, 4 red balls and 5 black
balls. A ball is picked, its color recorded and returned to the
box(with replacement). Another ball is then selected and its color
recorded.
1. Find the probability that 2 black balls are selected.
2. Find the probability that 2 balls of the same color are
selected.
Now 4 balls are picked with replacement
3.Find the probability no red balls are selected.
4.Find the probability that the...

Assume that the box contains 6 balls: 2 blue, 2 red, and 2
green. Balls are drawn in succession without replacement, and their
colors are noted until a blue ball is drawn. (1) Which of the
following is not a valid outcome for this experiment? A. GB B. B C.
RRGB D. GGG
(2) How many outcomes are there in the sample space?

Two marbles are drawn without replacement from a box with 3
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both marbles are white.

1. An urn contains two red, one purple, and two green marbles.
Two marbles are randomly drawn in succession without replacement.
Determine the probability that the first marble is green and the
second is red.
2. An urn contains two red, two purple, and two green marbles.
Two marbles are randomly drawn in succession
without replacement. Determine the probability
that both marbles are red.

An urn contains 8 white balls and 4 red balls. The experiment
consists of drawing 2 balls at random from the urn without
replacement.
a) What is the probability that both will be the same color?
b) Same question for part A, but with replacement.

2. Box A contains 10 red balls, and 15 green balls. Box B
contains 12 red balls and 17 balls
green. A ball is taken randomly from box A and then returned to box
B.
From box B a random ball is drawn.
a) Determine the chance that two green balls are taken.
b) Determine the chance that 1 red ball is drawn and 1 green ball
is taken

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