Question 1

Cross County Bicycles makes two mountain bike models that each come in three colors.The following table shows the production volumes for last week:  Based on the relative frequency assessment method,what is the probability that a manufactured item is brown?
A)0.2088
B)0.3819
C)0.3157
D)0.1324

Accepted Answer

To use the relative frequency assessment method, we need to calculate the proportion of items that are brown.

Total production volume = 2 models x 3 colors x 694 = 4164 
Frequency of brown = 2 models x 694 x 0.15 = 208.2

Proportion of brown = frequency of brown / total production volume = 208.2 / 4164 = 0.3157

Therefore, the probability that a manufactured item is brown is 0.3157, which corresponds to choice C.

Question 2

The college basketball team at West Texas State University has 10 players;5 are seniors,2 are juniors,and 3 are sophomores.Two players are randomly selected to serve as captains for the next game.What is the probability that both players selected are seniors?
A)0.22
B)0.33
C)0.50
D)0.66

Accepted Answer

The answer of The college basketball team at West Texas...

Question 3

Micron Technology has sales offices located in four cities: Dallas,Seattle,Boston,and Los Angeles.An analysis of the company's accounts receivables reveals the number of overdue invoices by days,as shown here.  Assume the invoices are stored and managed from a central database.
What is the probability that a randomly selected invoice from the database is from the Boston sales office?
A)0.2702
B)0.0231
C)0.3461
D)0.7765

Accepted Answer

The answer of Micron Technology has sales offices located in...

Question 4

Based on weather data collected in Racine,Wisconsin,on Christmas Day,the weather had the following distribution:  Based on the data,what is the probability that next Christmas will be rainy or cloudy and dry?
A)0.45
B)0.50
C)0.60
D)0.70

Accepted Answer

The answer of Based on weather data collected in Racine,Wisconsin,on...

Question 5

The results of a census of 2,500 employees of a mid-sized company with 401(k)retirement accounts are as follows:  Suppose researchers are going to sample employees from the company for further study.
Compute the probability that a randomly selected employee will be a female with an account balance between $50,000 and $99,999.
A)0.1580
B)0.1040
C)0.6160
D)0.4040

Accepted Answer

The answer of The results of a census of 2,500...

Question 6

Micron Technology has sales offices located in four cities: Dallas,Seattle,Boston,and Los Angeles.An analysis of the company's accounts receivables reveals the number of overdue invoices by days,as shown here.  Assume the invoices are stored and managed from a central database.
If a randomly selected invoice is from the Los Angeles office,what is the probability that it is 60 or fewer days overdue?
A)0.2702
B)0.0231
C)0.3461
D)0.7765

Accepted Answer

The answer of Micron Technology has sales offices located in...

Question 7

Based on weather data collected in Racine,Wisconsin,on Christmas Day,the weather had the following distribution:  Supposing next Christmas is dry,determine the probability that it will also be cloudy.
A)0.45
B)0.50
C)0.60
D)0.70

Accepted Answer

From the given distribution, we can see that the probability of it being dry and cloudy together is 0.6. So, if we suppose next Christmas is dry (which is given in the question), the probability that it will also be cloudy is 0.6. Therefore, the best choice is C) 0.60.

Question 8

The results of a census of 2,500 employees of a mid-sized company with 401(k)retirement accounts are as follows:  Suppose researchers are going to sample employees from the company for further study.
Based on the relative frequency assessment method,what is the probability that a randomly selected employee will have a 401(k)account balance of between $25,000 and $49,999?
A)0.1580
B)0.1040
C)0.6160
D)0.4040

Accepted Answer

To use the relative frequency assessment method, we need to calculate the proportion of employees with 401(k) account balances between $25,000 and $49,999.

From the table, we can see that there are 466 employees with balances between $25,000 and $49,999.

So, the proportion of employees with balances in this range is:

466/2500 = 0.1864

Therefore, the probability of randomly selecting an employee with a balance in this range is approximately 0.1864 or 0.1580 when rounded to the nearest thousandth.

Thus, the correct answer is A) 0.1580.

Question 9

Micron Technology has sales offices located in four cities: Dallas,Seattle,Boston,and Los Angeles.An analysis of the company's accounts receivables reveals the number of overdue invoices by days,as shown here.  Assume the invoices are stored and managed from a central database.
What is the probability that a randomly selected invoice from the database is over 90 days old and from the Seattle office?
A)0.2702
B)0.0231
C)0.3461
D)0.7765

Accepted Answer

To find the probability that a randomly selected invoice is over 90 days old and from the Seattle office, we need to use the information given in the table. From the table, we see that there are 57 invoices over 90 days old and 14 of them are from the Seattle office. Therefore, the probability of selecting an invoice that is both over 90 days old and from the Seattle office is:

P(over 90 days and from Seattle) = (number of invoices over 90 days and from Seattle) / (total number of invoices)
= 14 / 607
= 0.0231

Therefore, the best choice is B.

Question 10

Three events occur with probabilities P(E₁)= 0.35,P(E₂)= 0.15,P(E₃)= 0.40.If the event B occurs,the probability becomes P(E₁|B)= 0.25,P(B)= 0.30.Calculate P(E₁ and B). A)0.575 B)0.075 C)0.021 D)0.475

Accepted Answer

P(E₁ and B) = P(E₁|B) * P(B) = 0.25 * 0.30 = 0.075.

Question 11

Micron Technology has sales offices located in four cities: Dallas,Seattle,Boston,and Los Angeles.An analysis of the company's accounts receivables reveals the number of overdue invoices by days,as shown here.  Assume the invoices are stored and managed from a central database.
What is the probability that a randomly selected invoice from the database is between 30 and 90 days overdue?
A)0.2702
B)0.0231
C)0.3461
D)0.7765

Accepted Answer

To find the probability of a randomly selected invoice between 30 and 90 days overdue, we need to find the total number of invoices that are between 30 and 90 days overdue and divide it by the total number of invoices. 
Total number of invoices between 30 and 90 days overdue = 1,550 + 1,100 + 1,530 + 960 = 5,140 
Total number of invoices = 5,140 + 1,120 + 4,760 + 1,430 = 12,450 
Probability of a randomly selected invoice between 30 and 90 days overdue = 5,140 / 12,450 = 0.3461 
Therefore, the best choice is C.

Question 12

Three events occur with probabilities P(E₁)= 0.35,P(E₂)= 0.15,P(E₃)= 0.40.If the event B occurs,the probability becomes P(E₁|B)= 0.25,P(B)= 0.30. Assume that E₁,E₂,and E₃ are independent events.Calculate P(E₁ and E₂ and E₃). A)0.575 B)0.075 C)0.021 D)0.475

Accepted Answer

Since the events E₁, E₂, and E₃ are independent, we can simply multiply their individual probabilities to get the probability of all three events occurring: P(E₁ and E₂ and E₃) = P(E₁) * P(E₂) * P(E₃) = 0.35 * 0.15 * 0.4 = 0.021 Therefore, the answer is C.

Question 13

Cross County Bicycles makes two mountain bike models that each come in three colors.The following table shows the production volumes for last week:  What is the joint probability that a product manufactured is a YZ-99 and brown?
A)0.2088
B)0.3819
C)0.3157
D)0.1324

Accepted Answer

The answer of Cross County Bicycles makes two mountain bike...

Question 14

Based on weather data collected in Racine,Wisconsin,on Christmas Day,the weather had the following distribution:  /Thompson_sn3t_WordExports/Thompson_sn3t_WordExports
Based on these data,what is the probability that next Christmas will be dry?
A)0.45
B)0.50
C)0.60
D)0.70

Accepted Answer

The answer of Based on weather data collected in Racine,Wisconsin,on...

Question 15

Ponderosa Paint and Glass carries three brands of paint.A customer wants to buy another gallon of paint to match paint she purchased at the store previously.She can't recall the brand name and does not wish to return home to find the old can of paint.So she selects two of the three brands of paint at random and buys them. What is the probability that she matched the paint brand?
A)3/2
B)2/3
C)1/9
D)3/4

Accepted Answer

There are three possible scenarios: she could have chosen two different brands, she could have chosen two cans of the same brand, or she could have chosen one can of the matching brand and one can of a non-matching brand. The only scenario where she doesn't match is if she chooses two different brands, which has a probability of 2/3. Therefore, the probability that she matches is the complement of this, which is 1 - 2/3 = 1/3. However, since she could have chosen either of the three brands to begin with, the final probability is 1/3 * 3 = 2/3.

Question 16

Ponderosa Paint and Glass carries three brands of paint.A customer wants to buy another gallon of paint to match paint she purchased at the store previously.She can't recall the brand name and does not wish to return home to find the old can of paint.So she selects two of the three brands of paint at random and buys them. Her husband also goes to the paint store and fails to remember what brand to buy.So he also purchases two of the three brands of paint at random.Determine the probability that both the woman and her husband fail to get the correct brand of paint.(Hint: Are the husband's selections independent of his wife's selections?)
A)3/2
B)2/3
C)1/9
D)3/4

Accepted Answer

Let's call the three brands of paint A, B, and C. The probability that the woman chooses two brands that are not the correct one is 2/3 (she has a 2/3 chance of not choosing the correct brand for the first can, and then a 2/3 chance of not choosing it for the second can). The probability that the husband chooses two brands that are not the correct one is also 2/3, assuming his choices are independent of his wife's. 
To find the probability that both events occur (i.e. that neither the woman nor her husband choose the correct brand), we multiply their probabilities together: 
P(both choose incorrectly) = 2/3 * 2/3 = 4/9 
So the probability that both the woman and her husband fail to get the correct brand of paint is 4/9, which is equivalent to choice C.

Question 17

Three events occur with probabilities P(E₁)= 0.35,P(E₂)= 0.15,P(E₃)= 0.40.If the event B occurs,the probability becomes P(E₁|B)= 0.25,P(B)= 0.30.Compute P(E₁ or B). A)0.575 B)0.075 C)0.021 D)0.475

Accepted Answer

P(E₁ or B) = P(E₁) + P(B) - P(E₁ and B). P(E₁ and B) = P(E₁|B) * P(B) = 0.25 * 0.30 = 0.075. Therefore, P(E₁ or B) = 0.35 + 0.30 - 0.075 = 0.575.

Question 18

Cross County Bicycles makes two mountain bike models that each come in three colors.The following table shows the production volumes for last week:  What is the probability that the product manufactured is a YZ-99?
A)0.2088
B)0.3819
C)0.3157
D)0.1324

Accepted Answer

The answer of Cross County Bicycles makes two mountain bike...

Question 19

The Jack In The Box franchise in Bangor,Maine,has determined that the chance a customer will order a soft drink is 0.90.The probability that a customer will order a hamburger is 0.60.The probability that a customer will order french fries is 0.50. If a customer places an order,what is the probability that the order will include a soft drink and no fries if these two events are independent?
A)0.45
B)0.50
C)0.65
D)0.70

Accepted Answer

We can use the formula for the probability of independent events:
P(A and B) = P(A) * P(B)
Where A is the event of ordering a soft drink and B is the event of not ordering fries (i.e. the complement of the event of ordering fries). 
We want to find P(A and B), which is the probability of ordering a soft drink and not ordering fries. We are given P(A) = 0.90 and P(B) = 1 - P(ordering fries) = 1 - 0.50 = 0.50. 
Thus, using the formula for independent events:
P(A and B) = P(A) * P(B) = 0.90 * 0.50 = 0.45. 
Therefore, the answer is A) 0.45.

Question 20

The Jack In The Box franchise in Bangor,Maine,has determined that the chance a customer will order a soft drink is 0.90.The probability that a customer will order a hamburger is 0.60.The probability that a customer will order french fries is 0.50. The restaurant has also determined that if a customer orders a hamburger,the probability the customer will also order fries is 0.80.Determine the probability that the order will include a hamburger and fries.
A)0.45
B)0.58
C)0.68
D)0.48

Accepted Answer

The answer of The Jack In The Box franchise in...

Quiz 4: Introduction to Probability

Cross County Bicycles makes two mountain bike models that each come in three colors.The following table shows the production volumes for last week: Based on the relative frequency assessment method,what is the probability that a manufactured item is brown?

The college basketball team at West Texas State University has 10 players;5 are seniors,2 are juniors,and 3 are sophomores.Two players are randomly selected to serve as captains for the next game.What is the probability that both players selected are seniors?

Based on weather data collected in Racine,Wisconsin,on Christmas Day,the weather had the following distribution: Based on the data,what is the probability that next Christmas will be rainy or cloudy and dry?

Based on weather data collected in Racine,Wisconsin,on Christmas Day,the weather had the following distribution: Supposing next Christmas is dry,determine the probability that it will also be cloudy.

Three events occur with probabilities P(E₁) = 0.35,P(E₂) = 0.15,P(E₃) = 0.40.If the event B occurs,the probability becomes P(E₁|B) = 0.25,P(B) = 0.30.Calculate P(E₁ and B) .

Three events occur with probabilities P(E₁) = 0.35,P(E₂) = 0.15,P(E₃) = 0.40.If the event B occurs,the probability becomes P(E₁|B) = 0.25,P(B) = 0.30. Assume that E₁,E₂,and E₃ are independent events.Calculate P(E₁ and E₂ and E₃) .

Cross County Bicycles makes two mountain bike models that each come in three colors.The following table shows the production volumes for last week: What is the joint probability that a product manufactured is a YZ-99 and brown?

Based on weather data collected in Racine,Wisconsin,on Christmas Day,the weather had the following distribution: /Thompson_sn3t_WordExports/Thompson_sn3t_WordExports Based on these data,what is the probability that next Christmas will be dry?

Three events occur with probabilities P(E₁) = 0.35,P(E₂) = 0.15,P(E₃) = 0.40.If the event B occurs,the probability becomes P(E₁|B) = 0.25,P(B) = 0.30.Compute P(E₁ or B) .

Cross County Bicycles makes two mountain bike models that each come in three colors.The following table shows the production volumes for last week: What is the probability that the product manufactured is a YZ-99?