ASSIGNMENT #3
1
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. The collection of all possible sample points in
an experiment
is
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a.
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the sample space
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b.
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a sample point
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c.
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an experiment
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d.
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the population
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2
. From a group of six people, two individuals are to be selected at random. How many possible selections are there?
3. Two events, A and B, are mutually exclusive and each have a
no
n
zero
probability. If event A is known to occur, the probability of the occurrence of event B is
a.
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one
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b.
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any positive value
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c.
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zero
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d.
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any value between 0 and 1
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4
. If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =
a.
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0.400
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b.
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0.16
9
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c.
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0.390
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d.
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0.650
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5. If P(A) = 0.4, P(B | A) = 0.35, P(A B) = 0.69, then P(B) =
a.
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0.14
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b.
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0.43
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c.
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0.75
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d.
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0.59
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6. Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is
a.
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much larger than one
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b.
zero
c.
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infinity
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d.
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none of these alternatives is correct
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7. Assume your favorite football team has 2 games left to finish the season. The outcome of each game can be win, lose or ti
e.
The number of possible outcomes is
8. If a coin is tossed three times, the likelihood of obtaining three heads in a row is
a.
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0.000
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b.
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0.500
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c.
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0.875
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d.
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0.125
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9. If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A ∩ B) =
a.
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0.76
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b.
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1.00
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c.
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0.24
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d.
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0.20
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10
. An automobile dealer has kept records on the customers who visited his showroom. 40% of the people who visited his dealership were female. Furthermore, his records show that 35% of the females who visited his dealership purchased an automobile, while 20% of the males who visited his dealership purchased an automobile. Given that an automobile is purchased at the dealership, what is the probability that the customer is a female?
a.
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0.080
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b.
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0.550
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c.
0.400
d.
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0.538
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11. A bank gives a test to screen prospective employees. Among those who perform their jobs satisfactorily, 65% pass the test. Among those who do not perform satisfactorily, 25% pass the test. According to the bank’s records, 90% of its employees perform their jobs satisfactorily. What is the probability that a prospective employee who passed the test will not perform satisfactorily?
a.
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0.028
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b.
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0.041
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c.
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0.025
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d.
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0.585
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12. How many committees consisting of 3 female and 5 male students can be selected from a group of 5 female and 8 male students?
a.
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200
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b.
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20,160
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c.
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396
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d.
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560
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e.
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66
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13. Consider the experiment of tossing a coin three times and recording the outcome. Compute the total number of possible outcomes. You might also want to list the possible outcomes – this will help you with the next several problems.
14. Refer to question 13. Define an event A = {HHH, TTT, HTH} and an event B = {HHH, HTH, HHT, TTH}. Compute P(A) and P(B).
a.
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P(A) = 3/8; P(B) =
1/2
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b.
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P(A) = 1/2; P(B) = 1/2
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c.
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P(A) = 3/4; P(B) = 1/2
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d.
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P(A) =
1/4
; P(B) =
1/4
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15. Refer to question 14. Compute P(AB).
a.
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1/4
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b.
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1/2
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c.
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3/4
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d.
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5/8
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e.
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1
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16. Refer to question 14. Compute P(BA).
a.
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1/4
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b.
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1/3
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c.
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2/3
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d.
3/4
e.
1
17. Refer to question 14. Are events A and B independent?
18. Refer to question 14. Are events A and B mutually exclusive?
a.
yes
b.
no
19. If a six-sided die is tossed two times, the probability of obtaining two “4s” in a row is
a.
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1/6
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b.
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1/36
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c.
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1/96
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d.
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1/216
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20. Events A and B are mutually exclusive. Which of the following statements is also true?
a.
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A and B are also independent.
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b.
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P(A B) = P(A)P(B)
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c.
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P(A B) = P(A) + P(B)
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d.
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P(A ∩ B) = P(A) + P(B)
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√
