MATH 302 MATH302 Quiz 2 (APUS)

MATH302 Quiz 2 (APUS)

1. 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:
2. If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is:
3. 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 .
4. 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?
5. The probability of an event and the probability of its complement always sum to:
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? 
7. 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 fewer than 25 batteries will last at least 8 hours?
8. The binomial distribution can occur in which of the following situations? 
   
   I. whenever we are interested in the number of events that occur over a given interval of time 
   II. whenever we sample from a population with only two types of members 
   III. whenever we perform a sequence of identical experiments, each of which has only two possible outcomes 
9. According to an Internet posting, 80% of adults enjoy drinking beer. A group of 7 adults is chosen randomly. The probability that no more than 3 of them enjoy drinking beer is:
10. 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 between 25 and 30 batteries (inclusive) will last at least 8 hours? 
11. 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. 
12. 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. 9.9
13. 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:
14. 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. 
15. 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. 
    
    If a set of six books is to be placed on a shelf, in how many ways can the six books be arranged? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry. 
16. 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. 
17. 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 lock on a bank vault consists of three dials, each with 30 positions, In order for the vault to open, each of the three dials must be in the correct position. How many different "dial combinations" are there for this lock? Place your answer in the blank. Do not use any decimal places or commas. For example, 12345 would be a legitimate entry. 1
18. 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. What is the probability that at least two of the three vice presidents can attend the meeting? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 would be a legitimate entry. .352
19. Jim and Mike go to a coffee shop during their lunch break and toss a coin to see who will pay. The probability that Mike will pay three days in a row is 0.125.
20. True or False: The probability of a success must remain the same for each trial in a binomial experiment.