Question 1

Determine whether the events are mutually exclusive
-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.

Question 2

Determine whether the events are mutually exclusive.
-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

The events are not mutually exclusive because numbers that are both even and multiples of 3 (such as 6 and 12) are included in both categories. To find the probability, list the even numbers (2, 4, 6, 8, 10, 12, 14) and the multiples of 3 (3, 6, 9, 12, 15). Combining these without repetition gives 10 unique numbers (2, 3, 4, 6, 8, 9, 10, 12, 14, 15) out of 15, so the probability is $\frac{10}{15} = \frac{2}{3}$.

Question 3

Determine whether the events are mutually exclusive
-Suppose you are playing a game of chance. If you bet $7 on a certain event, you will collect $280 (including your $7 bet)if you win. Find the odds used for determining the payoff.

Accepted Answer

The odds are calculated by dividing the total payout by the bet amount minus 1, which is (280/7) - 1 = 39:1.

Question 4

Answer the question
-Two white mice mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur color of the offspring depends on the pairs of fur-color genes that they receive. Assume that neither the white nor the black gene dominates. List the possible outcomes. W = white and B = black

Accepted Answer

Since the male has both a white (W) and a black (B) fur-color gene and the female has only white fur-color genes (WW), the possible offspring combinations are WW (white from both parents) and BW (black from the father and white from the mother). The black and white genes are co-dominant, allowing for both colors to be expressed in the genotype.

Question 5

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

Accepted Answer

The events are mutually exclusive because it is not possible to draw both a red ball and a blue ball from the same bag in one draw.

Question 6

Answer the question
-Find the odds against correctly guessing the answer to a multiple choice question with 4 possible answers.

Accepted Answer

The odds against correctly guessing are the ratio of the number of incorrect options to the correct one. With 4 possible answers and only 1 correct, there are 3 incorrect choices, making the odds against guessing correctly 3:1.

Question 7

Determine whether the events are mutually exclusive.
-A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 5 wood and 10 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 events "wood" and "defective" are not mutually exclusive because a racket can be both wood and defective. The probability of selecting a wood racket is 100/200 = 0.5, and the probability of selecting a defective racket is 15/200 = 0.075. The probability of selecting a wood and defective racket is 5/200 = 0.025. 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 + 0.075 - 0.025 = 0.55.

Question 8

Determine whether the events are mutually exclusive.
-Find $\mathrm { P } ( \overline { \mathrm { A } } )$, given that $\mathrm { P } ( \mathrm { A } ) = 0.662$.

Accepted Answer

$\mathrm { P } ( \overline { \mathrm { A } } ) = 1 - \mathrm { P } ( \mathrm { A } ) = 1 - 0.662 = 0.338.$

Question 9

Determine whether the events are mutually exclusive.
-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

The events are not mutually exclusive because there are face cards that are also spades (Jack, Queen, King of Spades). There are 12 face cards in total and 13 spades, but since 3 of the spades are also face cards, we don't double count them, leading to 12 + 10 = 22 favorable outcomes out of 52 cards, which simplifies to $\frac{11}{26}$.

Question 10

Determine whether the events are mutually exclusive
-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 mutually exclusive because it is not possible to get a full time day job as a teller with a bank and a full time day job as a cashier at a store at the same time.

Question 11

Determine whether the events are mutually exclusive.
-Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.206. Find the probability that in a given year it will not snow on January 1st in that town.

Accepted Answer

The events "it will snow" and "it will not snow" are mutually exclusive because they cannot happen at the same time. The probability that it will not snow is 1 - 0.206 = 0.794.

Question 12

Determine whether the events are mutually exclusive.
-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 are mutually exclusive because a person's birthday cannot be in May and not in May at the same time. The probability that a person's birthday is not in May is $\frac{365 - 31}{365} = \frac{334}{365}$, since May has 31 days and there are 365 days in a year (ignoring leap years).

Question 13

Determine whether the events are mutually exclusive.
-Get stung by a bee. Get stung by a wasp.

Accepted Answer

Events are mutually exclusive if they cannot happen at the same time. Getting stung by a bee and getting stung by a wasp are not mutually exclusive because they are independent events; one does not prevent the other from happening.

Question 14

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 odds against selecting someone who commutes by bicycle are the ratio of the probability of not selecting a bicycle commuter to the probability of selecting one. Since 10% (or 10 out of 100) commute by bicycle, 90% (or 90 out of 100) do not. Therefore, the odds against are 90:10, which simplifies to 9:1.

Question 15

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

Accepted Answer

Finding a ten dollar bill on the sidewalk and finding a ten dollar bill on the grass are not mutually exclusive events because both can happen independently without affecting the occurrence of the other.

Question 16

Determine whether the events are mutually exclusive.
-The probability that Luis will pass his statistics test is 0.42. Find the probability that he will fail his statistics test.

Accepted Answer

The events of passing and failing a test are mutually exclusive because they cannot happen at the same time. If the probability of passing is 0.42, then the probability of failing is 1 - 0.42 = 0.58.

Question 17

Determine whether the events are mutually exclusive.
-The table below describes the smoking habits of a group of asthma sufferers. $$\begin{array} { r | c c c c c } 
& \text { Nonsmoker } & \begin{array} { c } 
\text { Occasional } \
\text { smoker }
\end{array} & \begin{array} { c } 
\text { Regular } \
\text { smoker }
\end{array} & \begin{array} { c } 
\text { Heavy } \
\text { smoker }
\end{array} & \text { Total } \
\hline \text { Men } & 433 & 42 & 71 & 37 & 583 \
\text { Women } & 326 & 47 & 78 & 39 & 490 \
\text { Total } & 759 & 89 & 149 & 76 & 1073
\end{array}$$ If one of the 1073 people is randomly selected, find the probability that the person is a man or a heavy smoker.

Accepted Answer

The answer of Determine whether the events are mutually exclusive.
-The...

Question 18

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

Accepted Answer

Events are mutually exclusive if they cannot occur at the same time. Going to a formal dinner affair and wearing blue jeans are generally considered mutually exclusive because formal attire is expected at such events, not casual wear like blue jeans.

Question 19

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

Accepted Answer

Reading a book by Mark Twain and reading about Tom Sawyer are not mutually exclusive events because you can do both at the same time by reading "The Adventures of Tom Sawyer," which is a book by Mark Twain about Tom Sawyer.

Question 20

Determine whether the events are mutually exclusive.
-If $\mathrm { P } ( \mathrm { A } ) = \frac { 10 } { 11 }$, find $\mathrm { P } ( \overline { \mathrm { A } } )$.

Accepted Answer

$\mathrm { P } ( \overline { \mathrm { A } } ) = 1 - \mathrm { P } ( \mathrm { A } ) = 1 - \frac { 10 } { 11 } = \frac { 1 } { 11 }$.

Quiz 4: Probability

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

Determine whether the events are mutually exclusive. -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 mutually exclusive -Suppose you are playing a game of chance. If you bet $7 on a certain event, you will collect $280 (including your $7 bet) if you win. Find the odds used for determining the payoff.

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

Answer the question -Find the odds against correctly guessing the answer to a multiple choice question with 4 possible answers.

Determine whether the events are mutually exclusive. -A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 5 wood and 10 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 mutually exclusive. -Find $\mathrm { P } ( \overline { \mathrm { A } } )$ , given that $\mathrm { P } ( \mathrm { A } ) = 0.662$ .

Determine whether the events are mutually exclusive. -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?

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

Determine whether the events are mutually exclusive. -Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.206. Find the probability that in a given year it will not snow on January 1st in that town.

Determine whether the events are mutually exclusive. -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 mutually exclusive. -Get stung by a bee. Get stung by a wasp.

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?

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

Determine whether the events are mutually exclusive. -The probability that Luis will pass his statistics test is 0.42. Find the probability that he will fail his statistics test.

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

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

Determine whether the events are mutually exclusive. -If $\mathrm { P } ( \mathrm { A } ) = \frac { 10 } { 11 }$ , find $\mathrm { P } ( \overline { \mathrm { A } } )$ .