Question 1

For each numerical value assigned to the probability of an event, identify the verbal statements that are appropriate. 
  Verbal statements: (i) cannot be a probability, (ii) the event is very unlikely to happen, (iii) 50-50 chance of happening, (iv) sure to happen, (v) more likely to happen that not.
Write your answer using the Roman numeral, that is, i, ii, iii, iv or v.

Accepted Answer

Part A: i
Part B: v
Part C: iii
Part D: iv
Part E: v

Question 2

Construct a sample space for the following experiment.
From an urn with six balls labeled 1 through 6, five balls are chosen simultaneously. If an elementary outcome is given by the balls 2 and 5, denote it by 25, writing the numbers in ascending order.

Accepted Answer

{12345, 12346, 12356, 12456, 13456, 23456}

Question 3

There are five elementary outcomes in a sample space. If P(e₁) = 0.13, P(e₂) = 0.06, P(e₃) = 0.16, and P(e₄) = 0.1, what is the probability of e₅?

Accepted Answer

0.55

Question 4

Suppose S= {e₁, e₂, …., e₄}. If the simple events e₁, e₂, …., e₄ are all equally likely, what are the numerical values of P(e₁), P(e₂), …., P(e₄)? Round your answer to two decimal places.

Accepted Answer

The answer of Suppose S= {e₁, e₂, …., e₄}. If...

Question 5

Suppose S= {e₁, e₂ e₃} . If P(e₁) = 0.4 and P (e₃)= 0.5 what is the probability of e₂?

Accepted Answer

The sum of probabilities of all events in a sample space S must equal 1. Therefore, P(e₂) = 1 - P(e₁) - P(e₃) = 1 - 0.4 - 0.5 = 0.1.

Question 6

The sample space of an experiment is S= {e₁, e₂ e₃} . Is the following assignment of probabilities permissible? P(e₁)=0.2 , P(e₂)=0.5 , P(e₃)=0.2

Accepted Answer

The answer of The sample space of an experiment is...

Question 7

Express the following statement in terms of probability.
The odds are 7 to 8 that a South American team will win FIFA's World Cup.

Accepted Answer

The answer of Express the following statement in terms of...

Question 8

Jackson County, Florida, has a population of 49,656, among them, 10,030 are persons under 18 years old. Estimate the probability that a person from this county, chosen at random, is under 18 years old. Round your answer two decimal places.

Accepted Answer

The answer of Jackson County, Florida, has a population of...

Question 9

Consider the experiment of tossing a coin nine times. Find the probability of getting exactly one head.

Accepted Answer

The probability of getting exactly one head in nine tosses of a fair coin is calculated using the binomial probability formula: $ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} $. Here, $ n = 9 $, $ k = 1 $, and $ p = 0.5 $. So, $ P(X = 1) = \binom{9}{1} (0.5)^1 (0.5)^8 = 9 \times \frac{1}{512} = \frac{9}{512} $.

Question 10

A letter is chosen at random from the word "OHIO". What is the probability that it is a vowel ? Round your answer to two decimal places.

Accepted Answer

The answer of A letter is chosen at random from...

Question 11

The spades and diamonds of a playing cards deck are placed in two separate piles. One card is drawn from each pile. Assume that A = 1 (ace), J = 11 (jack), Q = 12 (queen), and K = 13 (king).
Consider the following events:
A: the sum equals 8
B: the sum is odd
C: the sum is prime
D: both cards are face cards (J, Q, or K)
A) Find P(A)
B) Find P(B)
C) Find P(C)
D) Find P(D)
Round your answers to three decimal places.

Accepted Answer

The answer of The spades and diamonds of a playing...

Question 12

An experiment consists of tossing a coin, rolling a die, and tossing a coin again.
A) What is the probability of getting a head, a tail, and a number less than 5?
B) What is the probability of getting a number larger than 5?
C) What is the probability of getting at most one head?
Write your answer as a fraction reduced to lowest terms.

Accepted Answer

The answer of An experiment consists of tossing a coin,...

Question 13

A population projection for the 50 states and DC are grouped in the following frequency table.
  (End point convention: lower point is included, upper is not.)
If one state is selected at random, what is the probability that the population prediction is:
(A) Under 9?
(B) Under 15 but not under 3?
(C) 12 or over?
Round your answers to three decimal places.

Accepted Answer

The answer of A population projection for the 50 states...

Question 14

Friends will be called, one after another, and asked to go on a weekend trip with you. You will call until one agrees to go (A) or four friends are asked. What is the tree diagram for the sample space for this experiment?

Accepted Answer

The answer of Friends will be called, one after another,...

Question 15

Pioneer Of The Nile (A), I Want Revenge (B), and Hold Me Back (C), were the three favorites to win the Kentucky Derby one year. According to an expert, they should arrive first, second and third, respectively.
The tree diagram for the sample space is given below.
A) Complete, the tree diagram from top to bottom
B) State the composition of the event E = [exactly two horses arrived in the predicted place]

Accepted Answer

The answer of Pioneer Of The Nile (A), I Want...

Question 16

Pioneer Of The Nile (A), I Want Revenge (B), and Old Me Back (C) were the three favorites to win the Kentucky Derby one year. According to an expert, they should arrive first, second and third, respectively.
Consider the event E = [exactly two of these horses arrived in the predicted place]. Find P(E). Round your answers to two decimal places when necessary.

Accepted Answer

The answer of Pioneer Of The Nile (A), I Want...

Question 17

The most basic event relations are: intersection, complement and ______.

Accepted Answer

The answer of The most basic event relations are: intersection,...

Question 18

The sample space is given by the first 15 positive integers.
Consider the events:
A = [odd integers] B = [prime integers]
Make a Venn diagram showing these events.

Accepted Answer

The answer of The sample space is given by the...

Question 19

The ______ of two events A and B, is the set of all elementary out comes that are in A and B.

Accepted Answer

The answer of The ______ of two events A and...

Question 20

The intersection of A and B means that both A and B occur.

Accepted Answer

The intersection of two sets A and B, denoted as A ∩ B, includes all elements that are common to both sets, meaning both A and B occur.

Quiz 4: Probability

Construct a sample space for the following experiment. From an urn with six balls labeled 1 through 6, five balls are chosen simultaneously. If an elementary outcome is given by the balls 2 and 5, denote it by 25, writing the numbers in ascending order.

There are five elementary outcomes in a sample space. If P(e₁) = 0.13, P(e₂) = 0.06, P(e₃) = 0.16, and P(e₄) = 0.1, what is the probability of e₅?

Suppose S= {e₁, e₂, …., e₄}. If the simple events e₁, e₂, …., e₄ are all equally likely, what are the numerical values of P(e₁), P(e₂), …., P(e₄)? Round your answer to two decimal places.

Suppose S= {e₁, e₂ e₃} . If P(e₁) = 0.4 and P (e₃) = 0.5 what is the probability of e₂?

The sample space of an experiment is S= {e₁, e₂ e₃} . Is the following assignment of probabilities permissible? P(e₁)=0.2 , P(e₂)=0.5 , P(e₃)=0.2

Express the following statement in terms of probability. The odds are 7 to 8 that a South American team will win FIFA's World Cup.

Jackson County, Florida, has a population of 49,656, among them, 10,030 are persons under 18 years old. Estimate the probability that a person from this county, chosen at random, is under 18 years old. Round your answer two decimal places.

Consider the experiment of tossing a coin nine times. Find the probability of getting exactly one head.

A letter is chosen at random from the word "OHIO". What is the probability that it is a vowel ? Round your answer to two decimal places.

Friends will be called, one after another, and asked to go on a weekend trip with you. You will call until one agrees to go (A) or four friends are asked. What is the tree diagram for the sample space for this experiment?

The most basic event relations are: intersection, complement and ______.

The sample space is given by the first 15 positive integers. Consider the events: A = [odd integers] B = [prime integers] Make a Venn diagram showing these events.

The ______ of two events A and B, is the set of all elementary out comes that are in A and B.

The intersection of A and B means that both A and B occur.

Quiz 4: Probability

Construct a sample space for the following experiment. From an urn with six balls labeled 1 through 6, five balls are chosen simultaneously. If an elementary outcome is given by the balls 2 and 5, denote it by 25, writing the numbers in ascending order.

There are five elementary outcomes in a sample space. If P(e1) = 0.13, P(e2) = 0.06, P(e3) = 0.16, and P(e4) = 0.1, what is the probability of e5?

Suppose S= {e1, e2, …., e4}. If the simple events e1, e2, …., e4 are all equally likely, what are the numerical values of P(e1), P(e2), …., P(e4)? Round your answer to two decimal places.

Suppose S= {e1, e2 e3} . If P(e1) = 0.4 and P (e3) = 0.5 what is the probability of e2?

The sample space of an experiment is S= {e1, e2 e3} . Is the following assignment of probabilities permissible? P(e1)=0.2 , P(e2)=0.5 , P(e3)=0.2

Express the following statement in terms of probability. The odds are 7 to 8 that a South American team will win FIFA's World Cup.

Jackson County, Florida, has a population of 49,656, among them, 10,030 are persons under 18 years old. Estimate the probability that a person from this county, chosen at random, is under 18 years old. Round your answer two decimal places.

Consider the experiment of tossing a coin nine times. Find the probability of getting exactly one head.

A letter is chosen at random from the word "OHIO". What is the probability that it is a vowel ? Round your answer to two decimal places.

Friends will be called, one after another, and asked to go on a weekend trip with you. You will call until one agrees to go (A) or four friends are asked. What is the tree diagram for the sample space for this experiment?

The most basic event relations are: intersection, complement and ______.

The sample space is given by the first 15 positive integers. Consider the events: A = [odd integers] B = [prime integers] Make a Venn diagram showing these events.

The ______ of two events A and B, is the set of all elementary out comes that are in A and B.

The intersection of A and B means that both A and B occur.

There are five elementary outcomes in a sample space. If P(e₁) = 0.13, P(e₂) = 0.06, P(e₃) = 0.16, and P(e₄) = 0.1, what is the probability of e₅?

Suppose S= {e₁, e₂, …., e₄}. If the simple events e₁, e₂, …., e₄ are all equally likely, what are the numerical values of P(e₁), P(e₂), …., P(e₄)? Round your answer to two decimal places.

Suppose S= {e₁, e₂ e₃} . If P(e₁) = 0.4 and P (e₃) = 0.5 what is the probability of e₂?

The sample space of an experiment is S= {e₁, e₂ e₃} . Is the following assignment of probabilities permissible? P(e₁)=0.2 , P(e₂)=0.5 , P(e₃)=0.2