Question

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 fourth ball selected is the first occurrence of the color white?

Answer #1

Number of white balls = 3

Number of red balls = 4

Number of black balls = 5

Total number of balls = 3 + 4 + 5 = 12

1. P(2 black balls are selected) = (5/12)^{2}

= **0.1736**

2. P(2 balls of same color) = (3/12)^{2} +
(4/12)^{2} + (5/12)^{2}

= **0.3472**

3. P(red ball) = 4/12 = 1/3

P(not a red ball) = 1 - 1/3 = 2/3

P(no red balls) = (2/3)^{4}

= **0.1975**

P(white) = 3/12 = 0.25

P(not white) = 1 - 0.25 = 0.75

P(fourth ball selected is the first occurrence of the color white) = P(first 3 balls are not white) x P(fourth ball is white)

= 0.75^{3} x 0.25

= **0.1055**

Box I contains 7 red and 3 black balls; Box II contains 4 red
and 5 black balls. After a randomly selected ball is transferred
from Box I to Box II, 2 balls are drawn from Box II without
replacement. Given that the two balls are red, what is the
probability a black ball was transferred?

1. A box contains 3 white and 2 black balls. The white balls are
labelled by 1, 2, and 3, and the black balls by 4 and 5. A ball is
randomly picked from the box. Let ? be the number shown on the
picked ball, and ? = 1 if the picked ball is black; ? = 0
otherwise. Find
a. ?(? = 1);
b. ?(? = 4, ? = 1);
c. ?(??);
d. ???(?|? = 4).

A box contains one white ball, two red balls, and three black
balls. Make a box model.
Five draws are made with replacement from the
box. Find the chance that:
a) A red ball is never drawn.
b) A black ball appears exactly three
times.
c) A white ball appears at least once.

A box contains 4 red and 6 black balls. Two balls are selected
one after the other,
a) What is the probability that the first ball selected is black
and the second ball selected is also black, if the selection is
done without replacement.
b) What is the probability that the first ball selected is black
and the second ball selected is red, if the selection is done
without replacement.
c) What is the probability that the first ball selected...

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

An urn contains 1 white, 2 black, 3 red, and 4 green balls. If 6
balls are selected randomly (without replacement) and X represents
the number of selections that are either red or green, find: (a)
the probability mass function for X. (b) the expected value of X
(calculate this value directly by using the probability mass
function from part a).

Urn 1 contains 4 red balls and 3 black balls. Urn 2 contains 1
red ball and 3 black balls. Urn 3 contains 4 red balls and 2
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 fraction in simplest form or a decimal
rounded to 3 decimal places.
P(red)=

A box contains 8 red and 5 white balls. 8 balls are selected at
random, without replacement. Find the probability that 3 white
balls are selected.

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
jar together with another ball of the opposite color. In other
words, if a red ball is drawn it is returned to the jar together
with another black ball; if black ball is drawn it is returned to
the jar together...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 13 minutes ago

asked 13 minutes ago

asked 28 minutes ago

asked 29 minutes ago

asked 38 minutes ago

asked 40 minutes ago

asked 41 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago