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Sue has 10 pictures but only has space in her apartment to hang 4 of them on a wall. The number of different arrangements of four pictures from a selection of ten pictures is:

If A and B are any two events with P(A) = .8 and P(B|A) = .4, then the joint probability of A and B is

A gumball machine contains 300 grape flavored balls, 400 cherry flavored balls, and 500 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine?

If P(A) = P(A|B), then events A and B are said to be

A jar contains four white marbles, five red marbles, and six black marbles. If a marble is selected at random, find the probability that it is white or black .

Part 2 of 6 –

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30. 

What is the probability that greater than 30 batteries will last at least 8 hours?

The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months.

What is the standard deviation of X?

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30. 

What is the probability that greater than 40 batteries will last at least 8 hours?

A die is rolled 360 times. Find the standard deviation for the number of 3s that will be rolled.

A pet supplier has a stock of parakeets of which 10% are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet?

Part 3 of 6 –

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months. 

What is the variance of X?  Place your answer, rounded to two decimal places in the blank. For example, 4.56 would be a legitimate entry. 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

Find the mean of the following probability distribution?

Place your answer, rounded to two decimal places, in the blank.    When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 1.23 would be a legitimate entry. 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

A DVD rental business determines that customers will rent X number of DVDs according to the following distribution:

What is the mean number of DVDs that customers rent? Round your answer to one decimal place as necessary. For example, 4.5 would be a legitimate entry. 

Answer:   

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

In a survey, 55% of the voters support a particular referendum. If 40 voters are chosen at random, and X is the number of voters that support this referendum, find the mean and variance of X. Place the mean in the first blank 22 and place the variance in the second blank.  

Part 4 of 6 –

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

 = chocolate chosen

 = strawberry chosen

 = vanilla chosen

 = ice cream on a cone

icecreamina cup

Find the probability that the ice cream was vanilla flavor, given that it was sold in a cup.  Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry. 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

 = chocolate chosen

 = strawberry chosen

 = vanilla chosen

 = ice cream on a cone

ice cream in a cup

Find the probability that the ice cream was strawberry flavor, given that it was sold on a cone. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry. 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

A particular brand of women’s jeans is available in seven different sizes, three different colors, and three different styles. How many different jeans does the store manager need to order to have one pair of each type of jean? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry. 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

The president of a bank is attempting to arrange a meeting with the three vice presidents for a Friday weekly meeting. He believes that each of these three busy individuals, independently of the others, has about 40% chance of being able to attend the meeting. If the meeting will be held only if every vice president can attend, what is the probability that the meeting will take place? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 would be a legitimate entry. 

Part 5 of 6 –

Given that events A and B are independent and that P(A) = 0.8 and P(B|A) = 0.4, then P(A and B) = 0.32.

Part 6 of 6 –

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.