Question

What is the probability of each of the following?

a) rolling an odd number on a standard 6-sided die

b) rolling at least 2 on a standard 6-sided die

c) pulling a red ball from a bag containing 8 yellow, 6 red and 10 purple balls

d) randomly selecting your single favorite meal from a menu that includes 5 salads, 6 entrees, and 2 desserts.

Answer #1

**Solution:**

The possible outcomes on rolling a standard 6-sided die are:

a) rolling an odd number on a standard 6-sided die

**Answer:**

b) rolling at least 2 on a standard 6-sided die

**Answer:**

c) pulling a red ball from a bag containing 8 yellow, 6 red and 10 purple balls

**Answer:**

**The total number of balls in the bag is 8 + 6 + 10 =
24**

**The number of red balls is 6**

**Therefore, the probability of pulling a red ball
is:**

d) randomly selecting your single favorite meal from a menu that includes 5 salads, 6 entrees, and 2 desserts.

**Answer:** The total possible number of meals
are:

Therefore, the probability of randomly selecting your single favorite meal is:

Determine whether the following events are
disjoint.
(3)
Randomly drawing a spade from a deck of cards.
Randomly drawing a heart from a deck
of cards.
Randomly selecting a person born on January 25.
Randomly selecting a person that is 25
years old.
Rolling a 5 on a single roll of a six-sided die.
Rolling an odd number on a single roll
of a six-sided die.

An urn has 15 white balls, 13 green balls, 10 yellow balls, and
12 red balls. Determine the probability that it will come
out:
a. A red ball
b. A green ball
c. A white ball
d. A red ball and a yellow ball
e. A ball that is not green
Calculate the probability that the number 89 will come out when
taking a ball from a bag with 120 balls numbered from 1 to 120.
Calculate the probability that...

FIND EACH PROBABILITY
17. Selecting a Card- A card is selected at random from
a standard deck. Find each probability.
A. Randomly selecting a diamond or seven
B. Randomly selecting a red suit or a queen
C. Randomly Selecting a three or face card
18. Rolling a Die- You roll a die. Find each
probability.
A. Rolling a six or a number greater than four
B. Rolling a number less than five or an odd number
C. Rolling a three...

If there are 6 bags and each of them containing 6 balls.
Suppose x th bag is containing x red balls and 6-x blue
balls.
A fair die is roIled to obtain a number x in {1,2,...6}, and so
I pick a ball from x th bag.
Let Y=1 if a red ball is picked from x th bag andY=0 if blue
ball is picked.
1, E[y|x] and E[y]
2, var[y|x] and var[y]

You roll a six-sided die. Find the probability of each of the
following scenarios.
(a) Rolling a 6 or a number greater than 3
(b) Rolling a number less than 5 or an even number
(c) Rolling a 4 or an odd number

17. Selecting a Card- A card is selected at random from
a standard deck. Find each probability.
A. Randomly selecting a diamond or seven
B. Randomly selecting a red suit or a queen
C. Randomly Selecting a three or face card
18. Rolling a Die- You roll a die. Find each
probability.
A. Rolling a six or a number greater than four
B. Rolling a number less than five or an odd number
C. Rolling a three or an even...

Question 3: Consider the following experiment: A ball is drawn
from an urn containing 2 red balls, 2 white balls and 4 blue balls.
If the ball drawn is white, a fair coin is flipped and the outcome
is recorded. If the ball is blue, a card is drawn from a standard
(52 card) deck and the suit (club ♣, diamond ♦, heart ♥ and spade
♠, present in equal proportions in the deck) is recorded. If the
ball is...

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...

1. Suppose that A, B are two independent events, with
P(A) = 0.3 and P(B) = 0.4.
Find P(A and B)
a. 0.12
b. 0.3
c. 0.4
d. 0.70
2. Experiment: choosing a single ball from a bag which
has equal number of red, green, blue, and white ball and then
rolling a fair 6-sided die.
a.) List the sample space.
b.) What is the probability of drawing a green ball and
even number?
2.

For the following experiments list:
a) the possible events in the sample space; and b) the
probability of each event.
EXAMPLE: one flip of a normal coin.
Sample space: {heads, tails}
Probabilities: P(heads) = .5, P(tails) = .5
A random draw from a bag containing 8 red balls and 5 green
balls.
The simultaneous flip of two normal coins.
The flip of a coin and the roll of a normal 6-sided die.

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