Calculus and Probability

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The graph of a function f: [-2, p] -> R is shown below.
The average value of f over the interval [-2, p] is zero.
The area of the shaded region is 25/8.
If the graph is a straight line, for 0 <= x <= p, then the value of p is:

a. 2
b. 5
c. 5/4
d. 5/2
e. 25/4

The minimum number of times that a fair coin can be tossed so that the probability of obtaining a head on each trial is less than 0.0005 is:
a. 8
b. 9
c. 10
d. 11
e. 12

The sample space when a fair die is rolled is {1, 2, 3, 4, 5, 6}, with each outcome being equally likely. For which of the following pairs of events are the events independent?
a. {1. 2. 3} and {1, 2}
b. {1, 2} and {3, 4}
c. {1, 3, 5} and {1, 4, 6}
d. {1, 2} and {1, 3, 4, 6}
e. {1, 2} and {2, 4, 6}

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