# Mr Hyftvuihj'

Topics: Probability theory, Probability, Event Pages: 3 (818 words) Published: June 24, 2013
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Experiments, Counting Rules, and Assigning Probabilities

1. A corporation takes delivery of some new machinery that must be installed and checked before it becomes operational. The accompanying table shows a manager's probability assessment for the number of days required before the machinery becomes operational.

|Number of Days |3 |4 |5 |6 |7 | |Probability |.08 |.24 |.41 |.20 |.07 |

Let A be the event "It will be more than 4 days before the machinery becomes operational" and B the event "It will be less than 6 days before the machinery becomes available".

a) Find the probability of event A.
b) Find the probability of event B.
c) Describe the event that is the complement of event A.
d) Find the probability of the complement of event A.
e) Describe the event that is the intersection of events A and B.

2. A department store manager has monitored the numbers of complaints received per week about poor service. The probabilities for number of complaints in a week, established by this review, are shown below. Let A be the event "There will be at least one complaint in a week", and B the event "There will be less than 10 complaints in a week".

|Number of Complaints |0 |1-3 |4-6 |7-9 |10-12 |More than 12 | |Probability |.14 |.39 |.23 |.15 |.06 |.03 |

a) Find the probability of A.
b) Find the probability of B.
c) Find the probability of the complement of A.
d) Find the probability of the union of A and B.
e) Find the probability of the intersection of A and B.
f) Are A and B mutually exclusive?
g) Are A and B collectively exhaustive?

3. A company knows that a rival is about to bring out a competing product. It believes that this rival...