The following table provides the probabilities for the number of times that a ce
ID: 3298213 • Letter: T
Question
The following table provides the probabilities for the number of times that a certain computer system will crash in the course of a month. Let A be the event that there are more than two crashes during the month, and let B be the event that the system crashes at least once.
Number of Crashes
Probability
0
0.50
1
0.40
2
0.06
3
0.03
4
0.01
a) Is this a probability distribution?
b) Find a sample space.
c) Find the event A
d) Find the event B.
e) Find P(A)
f) Find P(B)
Number of Crashes
Probability
0
0.50
1
0.40
2
0.06
3
0.03
4
0.01
Explanation / Answer
a) This is a probability distribution since probability mass function is given
b) The sample space is {0,1,2,3,4}
c) A is the event that there are more than two crashes during the month i.e the rows corresponding to Number of crashes 3 and 4.
3
0.03
4
0.01
c) B is the event that the system crashes atleast once. This is all rows except the first i.e Number of crashes = 0.
1
0.40
2
0.06
3
0.03
4
0.01
d) P(A) = 0.03 + 0.01
= 0.04
e) P(B) = 1 - 0.50 = 0.50
3
0.03
4
0.01
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