Question 1

For a sample space {2,3,4,5,6}, two events are defined as follows:
Event A: A chosen number is greater than 4
Event B: A chosen number is a prime number; that is, 2, 3, or 5
Are those events A and B dependent or independent?

Accepted Answer

The answer of For a sample space {2,3,4,5,6}, two events...

Question 2

Suppose a trial consists of rolling two dice and reporting the smaller of the two numbers rolled. What are the possible outcomes? Are they equally likely?

Accepted Answer

The answer of Suppose a trial consists of rolling two...

Question 3

A game consists of tossing a coin and rolling a six-sided die. The results can be recorded easily; for example, if heads shows on the coin and a 4 shows on the die, you can record this as H4. List the sample space for the results of this game.

Accepted Answer

The answer of A game consists of tossing a coin...

Question 4

How many possible ways are there for drawing three spades from a regular (bridge) deck of cards?

Accepted Answer

The answer of How many possible ways are there for...

Question 5

A spinner numbered 1 through 10 is spun and one die is tossed simultaneously. The number spun and the number rolled are recorded. How many outcomes are in the sample space?

Accepted Answer

There are 10 possible outcomes for the spinner and 6 possible outcomes for the die. To find the total number of outcomes in the sample space, we multiply the number of outcomes for the spinner by the number of outcomes for the die: 10 x 6 = 60. Therefore, the answer is A, 60.

Question 6

What is the probability of drawing three cards that are all spades from a regular (bridge) deck of cards?

Accepted Answer

The answer of What is the probability of drawing three...

Question 7

Suppose you use a spinner to choose a random number between 0 and 1. Which is more likely-choosing a number between 1/3 and 2/3 or between 1/2 and 3/4?

Accepted Answer

The answer of Suppose you use a spinner to choose...

Question 8

Three dice are tossed. The number rolled on each die is recorded. How many outcomes are in the sample space?

Accepted Answer

For each die, there are six possible outcomes so for three dice, there are 6 x 6 x 6 = 216 possible outcomes in the sample space.

Question 9

A continuous probability model has a constant density curve on the range 0 to 12. What is the height of the density curve?

Accepted Answer

The answer of A continuous probability model has a constant...

Question 10

A spinner numbered 1 through 10 is spun and one die is rolled simultaneously. The sum of the number spun and the number rolled is recorded. How many outcomes are in the sample space?

Accepted Answer

There are 10 possible outcomes for spinning the spinner and 6 possible outcomes for rolling the die. Therefore, there are 10 x 6 = 60 possible outcomes for both events. However, some of these outcomes are duplicates, as the order in which the spinner and die are rolled does not matter for the sum. For example, the outcome of spinning a 3 and rolling a 4 is the same as spinning a 4 and rolling a 3. Since there are 10 possible sums ranging from 2 to 11, and each sum can be obtained in exactly one of 15 ways, the sample space has 15 outcomes.

Question 11

A game consists of tossing three coins. Find the probability model for the number of coins showing heads.

Accepted Answer

The answer of A game consists of tossing three coins....

Question 12

For a sample space {1,2,3,4,5,6,7,8}, two events are defined as follows:
Event A: A chosen number is greater than 4
Event B: A chosen number is a prime number; that is, 2, 3, 5, or 7
Are those events A and B dependent or independent?

Accepted Answer

The answer of For a sample space {1,2,3,4,5,6,7,8}, two events...

Question 13

A die is rolled and a coin is flipped simultaneously. The number rolled on the die and whether the coin lands heads or tails is recorded. How many outcomes are in the sample space?

Accepted Answer

The number of outcomes for rolling a die is 6, while the number of outcomes for flipping a coin is 2. Since these are happening simultaneously, we multiply the number of outcomes: 6 x 2 = 12. Therefore, there are 12 possible outcomes in the sample space.

Question 14

According to the central limit theorem, how does the standard deviation of averages over four observations compare with the standard deviation of individual observations?

Accepted Answer

The answer of According to the central limit theorem, how...

Question 15

Two coins are flipped at the same time and heads or tails is recorded. The sample space for this is:

Accepted Answer

The sample space for flipping two coins simultaneously includes all possible outcomes, which are HH (heads and heads), HT (heads and tails), TH (tails and heads), and TT (tails and tails). Therefore, the correct answer is C, which lists all possible outcomes of flipping two coins. A only includes one possible outcome (either heads or tails), B includes only combinations of two possible outcomes, and D includes duplicate outcomes.

Question 16

A football stadium snack bar conducted a survey and found that 30 customers bought one item, 52 customers bought two items, 21 customers bought three items, and 12 customers bought four items. What is the mean number of items purchased per customer? Round your answer to the nearest tenth.

Accepted Answer

The answer of A football stadium snack bar conducted a...

Question 17

The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 pounds, with a standard deviation of 0.35 pounds. The distribution of weights is approximately Normal. What is the probability that one potato chosen at random will weigh more than 1.65 pounds?

Accepted Answer

The answer of The mean weight of a collection of...

Question 18

In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm. Every hour a sample of 20 bearings is drawn, measured, and the mean diameter of the sample found. What is the standard deviation $\sigma$_x of the sample mean?

Accepted Answer

The answer of In the manufacturing process for ball bearings,...

Question 19

The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 pounds, with a standard deviation of 0.35 pounds. The distribution of weights is approximately Normal. What fraction of the potatoes in the shipment will weigh between 0.25 and 2.35 pounds?

Accepted Answer

The answer of The mean weight of a collection of...

Question 20

In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm. Between what two measurements will 95% of all diameters of ball bearings be found?

Accepted Answer

The answer of In the manufacturing process for ball bearings,...

Quiz 8: Probability: the Mathematics of Chance

For a sample space {2,3,4,5,6}, two events are defined as follows: Event A: A chosen number is greater than 4 Event B: A chosen number is a prime number; that is, 2, 3, or 5 Are those events A and B dependent or independent?

Suppose a trial consists of rolling two dice and reporting the smaller of the two numbers rolled. What are the possible outcomes? Are they equally likely?

A game consists of tossing a coin and rolling a six-sided die. The results can be recorded easily; for example, if heads shows on the coin and a 4 shows on the die, you can record this as H4. List the sample space for the results of this game.

How many possible ways are there for drawing three spades from a regular (bridge) deck of cards?

A spinner numbered 1 through 10 is spun and one die is tossed simultaneously. The number spun and the number rolled are recorded. How many outcomes are in the sample space?

What is the probability of drawing three cards that are all spades from a regular (bridge) deck of cards?

Suppose you use a spinner to choose a random number between 0 and 1. Which is more likely-choosing a number between 1/3 and 2/3 or between 1/2 and 3/4?

Three dice are tossed. The number rolled on each die is recorded. How many outcomes are in the sample space?

A continuous probability model has a constant density curve on the range 0 to 12. What is the height of the density curve?

A spinner numbered 1 through 10 is spun and one die is rolled simultaneously. The sum of the number spun and the number rolled is recorded. How many outcomes are in the sample space?

A game consists of tossing three coins. Find the probability model for the number of coins showing heads.

For a sample space {1,2,3,4,5,6,7,8}, two events are defined as follows: Event A: A chosen number is greater than 4 Event B: A chosen number is a prime number; that is, 2, 3, 5, or 7 Are those events A and B dependent or independent?

A die is rolled and a coin is flipped simultaneously. The number rolled on the die and whether the coin lands heads or tails is recorded. How many outcomes are in the sample space?

According to the central limit theorem, how does the standard deviation of averages over four observations compare with the standard deviation of individual observations?

Two coins are flipped at the same time and heads or tails is recorded. The sample space for this is:

A football stadium snack bar conducted a survey and found that 30 customers bought one item, 52 customers bought two items, 21 customers bought three items, and 12 customers bought four items. What is the mean number of items purchased per customer? Round your answer to the nearest tenth.

The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 pounds, with a standard deviation of 0.35 pounds. The distribution of weights is approximately Normal. What is the probability that one potato chosen at random will weigh more than 1.65 pounds?

In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm. Every hour a sample of 20 bearings is drawn, measured, and the mean diameter of the sample found. What is the standard deviation $\sigma$ _x of the sample mean?

The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 pounds, with a standard deviation of 0.35 pounds. The distribution of weights is approximately Normal. What fraction of the potatoes in the shipment will weigh between 0.25 and 2.35 pounds?

In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm. Between what two measurements will 95% of all diameters of ball bearings be found?

Quiz 8: Probability: the Mathematics of Chance

For a sample space {2,3,4,5,6}, two events are defined as follows: Event A: A chosen number is greater than 4 Event B: A chosen number is a prime number; that is, 2, 3, or 5 Are those events A and B dependent or independent?

Suppose a trial consists of rolling two dice and reporting the smaller of the two numbers rolled. What are the possible outcomes? Are they equally likely?

A game consists of tossing a coin and rolling a six-sided die. The results can be recorded easily; for example, if heads shows on the coin and a 4 shows on the die, you can record this as H4. List the sample space for the results of this game.

How many possible ways are there for drawing three spades from a regular (bridge) deck of cards?

A spinner numbered 1 through 10 is spun and one die is tossed simultaneously. The number spun and the number rolled are recorded. How many outcomes are in the sample space?

What is the probability of drawing three cards that are all spades from a regular (bridge) deck of cards?

Suppose you use a spinner to choose a random number between 0 and 1. Which is more likely-choosing a number between 1/3 and 2/3 or between 1/2 and 3/4?

Three dice are tossed. The number rolled on each die is recorded. How many outcomes are in the sample space?

A continuous probability model has a constant density curve on the range 0 to 12. What is the height of the density curve?

A spinner numbered 1 through 10 is spun and one die is rolled simultaneously. The sum of the number spun and the number rolled is recorded. How many outcomes are in the sample space?

A game consists of tossing three coins. Find the probability model for the number of coins showing heads.

For a sample space {1,2,3,4,5,6,7,8}, two events are defined as follows: Event A: A chosen number is greater than 4 Event B: A chosen number is a prime number; that is, 2, 3, 5, or 7 Are those events A and B dependent or independent?

A die is rolled and a coin is flipped simultaneously. The number rolled on the die and whether the coin lands heads or tails is recorded. How many outcomes are in the sample space?

According to the central limit theorem, how does the standard deviation of averages over four observations compare with the standard deviation of individual observations?

Two coins are flipped at the same time and heads or tails is recorded. The sample space for this is:

A football stadium snack bar conducted a survey and found that 30 customers bought one item, 52 customers bought two items, 21 customers bought three items, and 12 customers bought four items. What is the mean number of items purchased per customer? Round your answer to the nearest tenth.

The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 pounds, with a standard deviation of 0.35 pounds. The distribution of weights is approximately Normal. What is the probability that one potato chosen at random will weigh more than 1.65 pounds?

In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm. Every hour a sample of 20 bearings is drawn, measured, and the mean diameter of the sample found. What is the standard deviation σ\sigmaσ x of the sample mean?

The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 pounds, with a standard deviation of 0.35 pounds. The distribution of weights is approximately Normal. What fraction of the potatoes in the shipment will weigh between 0.25 and 2.35 pounds?

In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm. Between what two measurements will 95% of all diameters of ball bearings be found?

In the manufacturing process for ball bearings, the mean diameter is 5 mm with a standard deviation of 0.002 mm. Every hour a sample of 20 bearings is drawn, measured, and the mean diameter of the sample found. What is the standard deviation $\sigma$ _x of the sample mean?