Question 1

A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 5.

Accepted Answer

The probability of getting a 5 when rolling a die is 1 out of the 6 possible outcomes, so it is $\frac{1}{6}$.

Question 2

Which of the following probabilities for the sample points A, B, and C could be true if A, B, and C are the onlysample points in an experiment? .

Accepted Answer

The probabilities of all sample points in an experiment must sum to 1. Only choice A satisfies this condition, as $0 + \frac{1}{4} + \frac{3}{4} = 1$.

Question 3

In terms of probability, a(n) ___________________ is any process with uncertain results that can be repeated.

Accepted Answer

An experiment in probability is a process with uncertain results that can be repeated, such as rolling a die or flipping a coin.

Question 4

In a 1-pond bag of skittles the possible colors were red, green, yellow, orange, and purple. The probability ofdrawing a particular color from that bag is given below. Is this a probability model?
$$\begin{array} { | l | l | } 
\hline \text { Color } & \text { Probability } \
\hline \text { Red } & 0.2299 \
\hline \text { Green } & 0.1908 \
\hline \text { Orange } & 0.2168 \
\hline \text { Yellow } & 0.1889 \
\hline \text { Purple } & 0.1816 \
\hline
\end{array}$$

Accepted Answer

The sum of the probabilities is 1.007 (0.2299 + 0.1908 + 0.2168 + 0.1889 + 0.1816), which should equal 1 for a probability model. However, due to rounding errors, this slight deviation is acceptable, indicating it is intended to be a probability model.

Question 5

A(n) _______________ of a probability experiment is the collection of all outcomes possible.

Accepted Answer

The sample space of a probability experiment is the set of all possible outcomes of that experiment.

Question 6

The table below represents a random sample of the number of deaths per 100 cases for a certain illness overtime. If a person infected with this illness is randomly selected from all infected people, find the probabilitythat the person lives 3-4 years after diagnosis. Express your answer as a simplified fraction and as a decimal. $\begin{array}{l|l}
\text { Years after Diagnosis } & \text { Number deaths } \
\hline 1-2 & 15 \
3-4 & 35 \
5-6 & 16 \
7-8 & 9 \
9-10 & 6 \
11-12 & 4 \
13-14 & 2 \
15+ & 13
\end{array}$

Accepted Answer

The total number of cases is the sum of deaths in all time periods, which is $15 + 35 + 16 + 9 + 6 + 4 + 2 + 13 = 100$. The number of deaths in the 3-4 year period is 35. Therefore, the probability is $\frac{35}{100} = 0.35$.

Question 7

The probability that event A will occur is $$\mathrm { P } ( \mathrm { A } ) = \frac { \text { Number of successful outcomes } } { \text { Number of unsuccessful outcomes } }$$

Accepted Answer

The probability that event A will occur is actually $\mathrm { P } ( \mathrm { A } ) = \frac { \text { Number of successful outcomes } } { \text { Total number of possible outcomes } }$.

Question 8

A bag contains 25 wooden beads. The colors of the beads are red, blue, white, green, black, brown, and grey.The probability of randomly selecting a bead of a particular color from the bag is given below. Is this aprobability model?
$$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \text { Color } & \text { Red } & \text { Blue } & \text { White } & \text { Green } & \text { Black } & \text { Brown } & \text { Grey } \
\hline \text { Probability } & 0.28 & 0.24 & 0.20 & 0.16 & 0.12 & 0.08 & 0.03 \
\hline
\end{array}$$

Accepted Answer

The probabilities add up to 1, so it is a probability model.

Question 9

Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land onany one of the five numbered spaces. If the pointer lands on a borderline, spin again.  Find the probability that the arrow will land on 5 or 4.

Accepted Answer

The answer of Use the spinner below to answer the...

Question 10

If A, B, C, and D, are the only possible outcomes of an experiment, find the probability of D using the tablebelow. $\begin{array}{l|cccc}
\text { Outcome } & \text { A } & \text { B } & \text { C } & \text { D } \
\hline \text { Probability } & 1 / 7 & 1 / 7 & 1 / 7
\end{array}$

Accepted Answer

Since the probabilities of A, B, and C are each $1/7$, and these are the only outcomes besides D, the probability of D is $1 - (1/7 + 1/7 + 1/7) = 1 - 3/7 = 4/7$.

Question 11

An unusual event is an event that has a

Accepted Answer

An unusual event is one that has a low probability of occurrence, meaning it is not expected to happen often.

Question 12

Which of the following cannot be the probability of an event?

Accepted Answer

Probabilities range from 0 to 1, inclusive. A negative number like -59 cannot represent a probability.

Question 13

True or False: The probability of an event E in an empirical experiment may change from experiment toexperiment.

Accepted Answer

In empirical experiments, the probability of an event E can change based on the outcomes of previous experiments, as empirical probabilities are determined by the frequency of events occurring in a series of trials.

Question 14

The probability that event A will occur is $$\mathrm { P } ( \mathrm { A } ) = \frac { \text { Number of successful outcomes } } { \text { Total number of all possible outcomes } }$$

Accepted Answer

This formula correctly defines the probability of an event A occurring, where the probability is the ratio of the number of successful outcomes to the total number of all possible outcomes.

Question 15

With which model was the greatest percentage satisfied? Estimate the empirical probability that a person withthis model is very satisfied with the experience. Express the answer as a fraction with a denominator of 100.

Accepted Answer

The correct answer is Model A with a satisfaction rate expressed as a fraction $\frac{81}{100}$, indicating 81% satisfaction. The fraction is correctly expressed with a denominator of 100, matching the question's request for an empirical probability format.

Question 16

You are dealt one card from a standard 52-card deck. Find the probability of being dealt an ace or a 7.

Accepted Answer

There are 4 aces and 4 sevens in a 52-card deck, totaling 8 favorable outcomes. The probability is $\frac{8}{52} = \frac{2}{13}$.

Question 17

Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land onany one of the five numbered spaces. If the pointer lands on a borderline, spin again.  Find the probability that the arrow will land on an odd number.

Accepted Answer

The answer of Use the spinner below to answer the...

Question 18

The empirical probability that a person with a model shown is very satisfied with the experience is 10081 . Whatis the model?

Accepted Answer

The empirical probability of 10081 suggests a high satisfaction rate, which aligns with model A.

Question 19

Recently, the stock market took big swings up and down. A survey of 971 adult investors asked how often theytracked their portfolio. The table shows the investor responses. What is the probability that an adult investortracks his or her portfolio daily? Express your answer as a simplified fraction and as a decimal rounded tothree decimal places. $\begin{array}{l|l}
\text { How frequently? } & \text { Response } \
\hline \text { Daily } & 236 \
\hline \text { Weekly } & 261 \
\hline \text { Monthly } & 273 \
\hline \text { Couple times a year } & 141 \
\hline \text { Don't track } & 60
\end{array}$

Accepted Answer

The probability that an adult investor tracks his or her portfolio daily is calculated by dividing the number of daily trackers (236) by the total number of respondents (971), which simplifies to $\frac{236}{971}$ and rounds to 0.243 when expressed as a decimal.

Question 20

True or False: An outcome is any collection of events from a probability experiment.

Accepted Answer

An outcome is a specific result of a probability experiment. A collection of events is called an event.

Quiz 5: Probability