# Calculus and Probability

Please see the attachment for the full questions.

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}