Question 1

Determine whether the events are disjoint.
-If $\mathrm { P } ( \mathrm { A } ) = \frac { 14 } { 15 }$, find $\mathrm { P } ( \overline { \mathrm { A } } )$

Accepted Answer

Two events are disjoint (or mutually exclusive) if they cannot occur at the same time. In this case, we are not given any information about another event that could occur with event A, so we assume that event A is the only possible event. Therefore, the probability of the complement of event A, which is the event that A does not occur, is equal to the probability of all other possible outcomes. Since the sum of the probabilities of all possible outcomes is 1, we have:

$$\mathrm { P } ( \overline { \mathrm { A } } ) = 1 - \mathrm { P } ( \mathrm { A } ) = 1 - \frac{14}{15} = \frac{1}{15}$$

Therefore, the best choice is A.

Question 2

Answer the question.
-If you are told that a randomly selected mystery person was born in the 1990's, what is the probability of guessing his/her exact birth date (including year)?

Accepted Answer

Assuming that there are 365 days in a year, the probability of guessing the exact birth date of a randomly selected person is 1/365. Since the birth year is given to be in the 1990's, there are 365 days in each year from 1990 to 1999, inclusive. Therefore, the total number of possible birth dates is 10 * 365 = 3650. The probability of guessing the exact birth date is then 1/3650 = 2.738 x 10^-4. The closest value to this answer is D, so D is the best choice.

Question 3

Determine whether the events are disjoint.
-Draw one ball colored red from a bag. Draw one ball colored blue from the same bag.

Accepted Answer

The events are disjoint because it is impossible to draw a ball that is both red and blue at the same time from the bag. Therefore, if one event occurs (e.g. drawing a red ball), the other event (drawing a blue ball) cannot occur simultaneously.

Question 4

Find the indicated probability.
-A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?

Accepted Answer

There are 7 even numbers (2, 4, 6, 8, 10, 12, 14) and 5 multiples of 3 (3, 6, 9, 12, 15) on the spinner. However, the number 12 is counted twice in both groups, so we need to subtract one of them to avoid double counting. Thus, the total number of favorable outcomes is 7 + 5 - 1 = 11. The total number of possible outcomes is 15 (since there are 15 equal regions). Therefore, the probability is 11/15 or simplified to 2/3.

Question 5

Determine whether the events are disjoint.
-Read a book by Mark Twain. Read about Tom Sawyer.

Accepted Answer

The events are not disjoint as reading a book by Mark Twain and reading about Tom Sawyer can coincide since Tom Sawyer is a character from the book written by Mark Twain.

Question 6

Find the indicated probability.
-The table below describes the smoking habits of a group of asthma sufferers. $$\begin{array} { r | c c c c c } 
& \text { Nonsmoker } & \begin{array} { c } 
\text { Occasional } \
\text { smoker }
\end{array} & \begin{array} { c } 
\text { Regular } \
\text { smoker }
\end{array} & \begin{array} { c } 
\text { Heavy } \
\text { smoker }
\end{array} & \text { Total } \
\hline \text { Men } & 431 & 50 & 71 & 49 & 601 \
\text { Women } & 382 & 48 & 86 & 39 & 555 \
\text { Total } & 813 & 98 & 157 & 88 & 1156
\end{array}$$ If one of the 1156 people is randomly selected, find the probability that the person is a man or a heavy smoker.

Accepted Answer

The probability that the person is a man is 601/1156 = 0.520. The probability that the person is a heavy smoker is 88/1156 = 0.076. The probability that the person is a man or a heavy smoker is 0.520 + 0.076 - 0.004 = 0.592.

Question 7

Find the indicated probability.
-A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 7 wood and 14 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood
Or defective.

Accepted Answer

The probability that the racket is wood is 100/200 = 0.5. The probability that the racket is defective is (7+14)/200 = 0.105. Using the formula for the probability of either event occurring, P(A or B) = P(A) + P(B) - P(A and B), we get 0.5 + 0.105 - (7/200) = 0.57.

Question 8

Determine whether the events are disjoint.
-Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass.

Accepted Answer

The events are not disjoint because they can occur simultaneously; you can find a ten dollar bill that is partially on the sidewalk and partially on the grass.

Question 9

Find the indicated probability.
-If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade?

Accepted Answer

There are 12 face cards and 13 spades in a deck of 52 cards. However, we don't want to count the jack, queen, and king of spades twice, so we need to subtract the three spade face cards (jack, queen, king). Thus, the total number of cards that are either a face card or a spade is 12 + 13 - 3 = 22. The probability of picking one of these cards is then 22/52 = 11/26.

Question 10

Answer the question.
-If an apple is hanging from a string and three flies land on it, find the probability that all three are on points that are within the same hemisphere.

Accepted Answer

Since the apple is hanging, we can consider it as a sphere. If we divide the sphere into two hemispheres, the probability that the first fly lands in one hemisphere is 1/2. The second fly also has a probability of 1/2 of landing in the same hemisphere as the first fly. Similarly, the third fly has a probability of 1/2 of landing in the same hemisphere as the first two flies. Therefore, the probability that all three flies are on points that are within the same hemisphere is (1/2) x (1/2) x (1/2) = 1/8. However, there are two hemispheres where the flies can land, so we need to double the probability to get 1/4, which is answer choice C.

Question 11

Determine whether the events are disjoint.
-If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

Accepted Answer

The events "having a birthday in May" and "not having a birthday in May" are disjoint, meaning they cannot happen at the same time. Therefore, the probability of not having a birthday in May is equal to 1 minus the probability of having a birthday in May. Since May has 31 days out of 365, the probability of having a birthday in May is $\frac{31}{365}$, so the probability of not having a birthday in May is $1-\frac{31}{365}=\frac{334}{365}$.

Question 12

Determine whether the events are disjoint.
-The probability that Luis will pass his statistics test is 0.49. Find the probability that he will fail his statistics test.

Accepted Answer

To find the probability of Luis failing his statistics test, we can use the fact that the sum of the probabilities of all possible outcomes is 1. Since passing and failing the test are the only two possible outcomes, we can subtract the probability of passing from 1 to find the probability of failing:
P(fail) = 1 - P(pass) = 1 - 0.49 = 0.51
Therefore, the best choice is A) 0.51.

Question 13

Determine whether the events are disjoint.
-Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.428. Find the probability that in a given year it will not snow on January 1st in that town.

Accepted Answer

The probability of an event and its complement always add up to 1, so the probability of not snowing on January 1st would be 1 - 0.428 = 0.572. Therefore, the best choice is B.

Question 14

Answer the question.
-Suppose you are playing a game of chance. If you bet $5 on a certain event, you will collect $115 (including your $5 bet) if you win. Find the odds used for determining the payoff.

Accepted Answer

The odds used for determining the payoff can be found by dividing the total amount you collect ($115) by the amount of your bet ($5):

$115/$5 = 23

So the odds used are 23:1. However, the question is asking for the odds used for determining the payoff, not the actual odds of winning. To find this, you subtract 1 from the first part of the ratio:

23-1 = 22

Therefore, the answer is B: 22:1.

Question 15

Determine whether the events are disjoint.
-Go to a formal dinner affair. Wear blue jeans.

Accepted Answer

The two events are completely unrelated and it is impossible to do both simultaneously. Therefore, they are disjoint.

Question 16

Determine whether the events are disjoint.
-Find $P ( \bar { A } )$, given that $P ( A ) = 0.493$.

Accepted Answer

The events are disjoint if they cannot occur at the same time. The probability of the complement of event A, $P(\bar{A})$, is calculated as $1 - P(A)$. Thus, $P(\bar{A}) = 1 - 0.493 = 0.507$.

Question 17

Determine whether the events are disjoint.
-Get a full time day job as a teller with a bank. Get a full time day job as a cashier at a store.

Accepted Answer

The events are disjoint because you cannot simultaneously have a full time day job as a teller with a bank and a full time day job as a cashier at a store. Choosing one event excludes the possibility of the other event occurring. Therefore, the best choice is to select one option over the other.

Question 18

Answer the question.
-In a certain town, 10% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?

Accepted Answer

The answer of Answer the question.
-In a certain town, 10%...

Question 19

Answer the question.
-Find the odds against correctly guessing the answer to a multiple choice question with 6 possible answers.

Accepted Answer

The odds against guessing correctly are calculated as the ratio of incorrect outcomes to correct outcomes. With 6 possible answers, only 1 is correct, so there are 5 incorrect answers. Thus, the odds against guessing correctly are 5:1.

Question 20

Determine whether the events are disjoint.
-Meet a man with an umbrella. Meet a man with a raincoat.

Accepted Answer

The events are not mutually exclusive because it is possible to meet a man who is wearing both an umbrella and a raincoat at the same time.

Quiz 4: Probability

Determine whether the events are disjoint. -If $\mathrm { P } ( \mathrm { A } ) = \frac { 14 } { 15 }$ , find $\mathrm { P } ( \overline { \mathrm { A } } )$

Answer the question. -If you are told that a randomly selected mystery person was born in the 1990's, what is the probability of guessing his/her exact birth date (including year) ?

Determine whether the events are disjoint. -Draw one ball colored red from a bag. Draw one ball colored blue from the same bag.

Find the indicated probability. -A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?

Determine whether the events are disjoint. -Read a book by Mark Twain. Read about Tom Sawyer.

Find the indicated probability. -A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 7 wood and 14 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood Or defective.

Determine whether the events are disjoint. -Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass.

Find the indicated probability. -If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade?

Answer the question. -If an apple is hanging from a string and three flies land on it, find the probability that all three are on points that are within the same hemisphere.

Determine whether the events are disjoint. -If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

Determine whether the events are disjoint. -The probability that Luis will pass his statistics test is 0.49. Find the probability that he will fail his statistics test.

Determine whether the events are disjoint. -Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.428. Find the probability that in a given year it will not snow on January 1st in that town.

Answer the question. -Suppose you are playing a game of chance. If you bet $5 on a certain event, you will collect $115 (including your $5 bet) if you win. Find the odds used for determining the payoff.

Determine whether the events are disjoint. -Go to a formal dinner affair. Wear blue jeans.

Determine whether the events are disjoint. -Find $P ( \bar { A } )$ , given that $P ( A ) = 0.493$ .

Determine whether the events are disjoint. -Get a full time day job as a teller with a bank. Get a full time day job as a cashier at a store.

Answer the question. -In a certain town, 10% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?

Answer the question. -Find the odds against correctly guessing the answer to a multiple choice question with 6 possible answers.

Determine whether the events are disjoint. -Meet a man with an umbrella. Meet a man with a raincoat.