Question 1

There are 3 balls in a hat; one with the number 2 on it,one with the number 6 on it,and one with the number 8 on it.You pick a ball from the hat at random and then you flip a coin.Using a tree diagram ,obtain the sample space for the experiment.List the elements that make up the sample space.
A)2 H T,6 H T,8 H T
B)2 H,6 H,8 H
C)2 6 8 H,2 6 8 T
D)2 H,2 T,6 H,6 T,8 H,8 T

Accepted Answer

The sample space consists of all possible outcomes of picking a ball and flipping a coin. There are 3 possible outcomes for picking a ball (2, 6, or 8) and 2 possible outcomes for flipping a coin (heads or tails), so the total sample space has 3x2=6 elements. Therefore, the correct answer is D, which lists all 6 possible outcomes: 2H, 2T, 6H, 6T, 8H, and 8T.

Question 2

Find the odds.
-If the sectors are of equal size,what are the odds of spinning an A on this spinner? 
A)2:6
B)3:5
C)6:2
D)4:2

Accepted Answer

Since the sectors are of equal size, each sector has an equal chance of landing on the spinner. There are a total of 8 sectors and only 3 of them have an A. Therefore, the odds of spinning an A are 3/8. This can be simplified to 3:5. So, the best choice is B)3:5.

Question 3

List the outcomes of the sample space.
-A box contains 10 blue cards numbered 1 through 10.List the sample space of picking one card from the box.
A){100}
B){1,2,3,4,5,6,7,8,9,10}
C){10}
D){8}

Accepted Answer

The sample space of picking one card from the box contains the numbers 1 through 10, so the correct option is B. Option A is incorrect because there are only 10 cards in the box, not 100. Option C is incorrect because it only includes the number 10. Option D is incorrect because it only includes the number 8.

Question 4

List the outcomes of the sample space.
-A box contains 10 red cards numbered 1 through 10.List the sample space of picking one card from the box.
A){10}
B){100}
C){1,10}
D){1,2,3,4,5,6,7,8,9,10}

Accepted Answer

The sample space of picking one card from the box is the set of numbers from 1 to 10, so the correct option is D. Option A only includes the number 10, option B is not feasible as there are only 10 cards in the box, and option C only includes the numbers 1 and 10.

Question 5

Find the probability.
-A sample of 4 different calculators is randomly selected from a group containing 10 that are defective and 28 that have no defects.What is the probability that at least one of the calculators is defective?
A)0.100
B)0.723
C)0.277
D)0.705

Accepted Answer

Probability of selecting all calculators with no defects is (28/38)^4. 
Therefore, probability of at least one defective calculator is 1 - (28/38)^4 = 0.723.

Question 6

List the outcomes of the sample space.
-A group of 18 songs are assigned numbers 1 through 18.List the outcomes of sample space of the event choosing a song with a number 5 or less.
A){1,2,3,4}
B){1,2,3,4,5}
C){18}
D){1}

Accepted Answer

The event is choosing a song with a number 5 or less. Outcomes with numbers 1,2,3,4,5 satisfy this condition. Hence, the correct choice is B.

Question 7

Find the odds.
-The probability of a person getting a job interview is 0.54.What are the odds against getting the interview?
A)54:100
B)23:54
C)1:54
D)23:27

Accepted Answer

The odds against getting the interview are calculated as the ratio of the probability of not getting the interview to the probability of getting the interview. The probability of not getting the interview is 1 - 0.54 = 0.46. Therefore, the odds against are 0.46:0.54, which simplifies to 23:27.

Question 8

Find the odds.
-In a certain town,20% of people commute to work by bus.If a person is selected randomly from the town,what are the odds against selecting someone who commutes by bus?
A)1:4
B)4:1
C)1:5
D)4:5

Accepted Answer

The probability of selecting someone who commutes by bus is 20% or 0.2. The probability of selecting someone who does not commute by bus is 1 - 0.2 = 0.8. The odds against selecting someone who commutes by bus are the ratio of the probability of not commuting by bus to the probability of commuting by bus, which is 0.8:0.2 or 4:1.

Question 9

Find the indicated probability.
-In a homicide case 3 different witnesses picked the same man from a line up.The line up contained 5 men.If the identifications were made by random guesses,find the probability that all 3 witnesses would pick the same
Person.
A)0.008
B)0.0041152
C)0.04
D)0.6

Accepted Answer

The probability that one witness picks the correct person by random guess is 1/5. For all three witnesses to pick the same person, the probability is (1/5)^3 = 0.008.

Question 10

In a survey of the number of DVDs in a house, the table shows the probabilities. 
-Find the probability of a house having 1 or 2 DVDs.
A)0.57
B)0.83
C)0.95
D)0.38

Accepted Answer

To find the probability of a house having 1 or 2 DVDs, we add the probabilities of P(1 DVD) and P(2 DVDs).

P(1 or 2 DVDs) = P(1 DVD) + P(2 DVDs) 
= 0.32 + 0.25 
= 0.57

Therefore, the probability of a house having 1 or 2 DVDs is 0.57, which corresponds to choice A.

Question 11

Find the odds.
-Suppose you are playing a game of chance.If you bet $9 on a certain event,you will collect $360(including your $9 bet)if you win.Find the odds used for determining the payoff.
A)39:1
B)1:39
C)360:369
D)40:1

Accepted Answer

The odds are determined by the ratio of the probability of winning to the probability of losing. In this case, if you bet $9 and can potentially win $360, your probability of winning must be 1/40 (since there are 40 possible outcomes - either you win or you lose). The odds can be expressed as the ratio of the probability of winning to the probability of losing (which is 39/1 or 39:1). Therefore, the correct answer is A) 39:1.

Question 12

Find the probability.
-Samantha is taking courses in math and English.The probability of passing math is estimated at 0.4 and English at 0.6.She also estimates that the probability of passing at least one of them is 0.8.What is her probability of passing both courses?
A)0
B)0.12
C)0.2
D)0.8

Accepted Answer

The probability of passing at least one course is given by the formula: P(Math or English) = P(Math) + P(English) - P(Math and English). Plugging in the values: 0.8 = 0.4 + 0.6 - P(Math and English). Solving for P(Math and English) gives 0.2.

Question 13

Find the probability.
-The table below describes the smoking habits of a group of asthma sufferers.  If one of the 1124 people is randomly selected,find the probability that the person is a man or a heavy smoker.
A)0.511
B)0.512
C)0.552
D)0.471

Accepted Answer

The answer of Find the probability.
-The table below describes the...

Question 14

List the outcomes of the sample space.
-A 6-sided die is rolled.The sides contain the numbers 1,2,3,4,5,6.List the sample space of rolling one die.
A){1,2,3,4,5,6}
B){36}
C){6}
D){1,2,6}

Accepted Answer

The sample space of rolling one die consists of the numbers 1, 2, 3, 4, 5, and 6, so the correct answer is A. B only represents the total number of outcomes possible when rolling two dice, while C and D are both subsets of the sample space and do not represent the entire set of outcomes.

Question 15

In a survey of the number of DVDs in a house, the table shows the probabilities. 
-Find the probability of a house having 3 or more DVDs.
A)0.57
B)0.83
C)0.05
D)0.38

Accepted Answer

The answer of In a survey of the number of...

Question 16

Find the probability.
-At the Stop 'n Go tune-up and brake shop,the manager has found that an SUV will require a tune-up with a probability of 0.6,a brake job with a probability of 0.1 and both with a probability of 0.02.What is the
Probability that an SUV requires either a tune-up or a brake job?
A)0.32
B)0.7
C)0.58
D)0.68

Accepted Answer

The probability of either event occurring is found using the formula P(A or B) = P(A) + P(B) - P(A and B). Here, P(tune-up) = 0.6, P(brake job) = 0.1, and P(both) = 0.02. So, P(tune-up or brake job) = 0.6 + 0.1 - 0.02 = 0.68.

Question 17

Find the probability.
-In a batch of 8,000 clock radios 6% are defective.A sample of 9 clock radios is randomly selected without replacement from the 8,000 and tested.The entire batch will be rejected if at least one of those tested is defective.What is the probability that the entire batch will be rejected?
A)0.573
B)0.111
C)0.0600
D)0.427

Accepted Answer

The probability of selecting a non-defective clock radio on the first test is 0.94 (1 - 0.06). The probability of selecting a non-defective clock radio on the second test is 0.933 (the batch is without replacement, so there is one fewer non-defective clock radio in the batch). Continue this process until the probability of selecting a non-defective clock radio on the ninth test is 0.88 (there are only 7992 clock radios left in the batch at this point).

To find the probability that at least one clock radio in the sample is defective, we can find the probability that all of them are non-defective and subtract that from 1:
P(at least one defective) = 1 - P(all non-defective)

P(all non-defective) = 0.94 * 0.933 * ... * 0.88
P(all non-defective) = 0.511

Therefore,
P(at least one defective) = 1 - P(all non-defective)
P(at least one defective) = 1 - 0.511
P(at least one defective) = 0.489

So the probability that the entire batch will be rejected is the same as the probability that at least one clock radio in the sample is defective, which is 0.489. Subtract this from 1 to get the probability that the entire batch will not be rejected:
P(batch not rejected) = 1 - 0.489
P(batch not rejected) = 0.511

Therefore, the probability that the entire batch will be rejected is:
P(batch rejected) = 1 - P(batch not rejected)
P(batch rejected) = 1 - 0.511
P(batch rejected) = 0.489, which is closest to choice D (0.427).

Question 18

A fair die and a fair coin are tossed in succession.Find the sample space composed of equally likely events.

Accepted Answer

The answer of A fair die and a fair coin...

Question 19

Find the probability.
-A study conducted at a certain college shows that 62% of the school's graduates find a job in their chosen field within a year after graduation.Find the probability that among 7 randomly selected graduates,at least one finds a job in his or her chosen field within a year of graduating.
A)0.143
B)0.999
C)0.965
D)0.620

Accepted Answer

The probability that a randomly selected graduate finds a job in their chosen field within a year of graduating is 0.62. The probability that a randomly selected graduate does not find a job in their chosen field within a year of graduating is 1 - 0.62 = 0.38. The probability that none of the 7 randomly selected graduates finds a job in their chosen field within a year of graduating is 0.38^7 = 0.001. The probability that at least one of the 7 randomly selected graduates finds a job in their chosen field within a year of graduating is 1 - 0.001 = 0.999.

Question 20

Find the odds.
-If two fair dice are thrown,what are the odds of obtaining a sum of 7?
A)3:4
B)1:6
C)1:5
D)5:1

Accepted Answer

There are a total of 36 possible outcomes when two dice are thrown (6 possible outcomes for each die thrown). The possible outcomes that result in a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are six possible outcomes that result in a sum of 7, so the odds of obtaining a sum of 7 are 6/36 or 1/6. Written in ratio form, the odds are 1:5. Therefore, the best choice is C) with odds of 1:5.

Quiz 8: Probability

There are 3 balls in a hat; one with the number 2 on it,one with the number 6 on it,and one with the number 8 on it.You pick a ball from the hat at random and then you flip a coin.Using a tree diagram ,obtain the sample space for the experiment.List the elements that make up the sample space.

Find the odds. -If the sectors are of equal size,what are the odds of spinning an A on this spinner?

List the outcomes of the sample space. -A box contains 10 blue cards numbered 1 through 10.List the sample space of picking one card from the box.

List the outcomes of the sample space. -A box contains 10 red cards numbered 1 through 10.List the sample space of picking one card from the box.

Find the probability. -A sample of 4 different calculators is randomly selected from a group containing 10 that are defective and 28 that have no defects.What is the probability that at least one of the calculators is defective?

List the outcomes of the sample space. -A group of 18 songs are assigned numbers 1 through 18.List the outcomes of sample space of the event choosing a song with a number 5 or less.

Find the odds. -The probability of a person getting a job interview is 0.54.What are the odds against getting the interview?

Find the odds. -In a certain town,20% of people commute to work by bus.If a person is selected randomly from the town,what are the odds against selecting someone who commutes by bus?

Find the indicated probability. -In a homicide case 3 different witnesses picked the same man from a line up.The line up contained 5 men.If the identifications were made by random guesses,find the probability that all 3 witnesses would pick the same Person.

In a survey of the number of DVDs in a house, the table shows the probabilities. -Find the probability of a house having 1 or 2 DVDs.

Find the odds. -Suppose you are playing a game of chance.If you bet $9 on a certain event,you will collect $360(including your $9 bet) if you win.Find the odds used for determining the payoff.

Find the probability. -Samantha is taking courses in math and English.The probability of passing math is estimated at 0.4 and English at 0.6.She also estimates that the probability of passing at least one of them is 0.8.What is her probability of passing both courses?

Find the probability. -The table below describes the smoking habits of a group of asthma sufferers. If one of the 1124 people is randomly selected,find the probability that the person is a man or a heavy smoker.

List the outcomes of the sample space. -A 6-sided die is rolled.The sides contain the numbers 1,2,3,4,5,6.List the sample space of rolling one die.

In a survey of the number of DVDs in a house, the table shows the probabilities. -Find the probability of a house having 3 or more DVDs.

Find the probability. -At the Stop 'n Go tune-up and brake shop,the manager has found that an SUV will require a tune-up with a probability of 0.6,a brake job with a probability of 0.1 and both with a probability of 0.02.What is the Probability that an SUV requires either a tune-up or a brake job?

A fair die and a fair coin are tossed in succession.Find the sample space composed of equally likely events.

Find the odds. -If two fair dice are thrown,what are the odds of obtaining a sum of 7?