Problem set 1

please answer all 8 questions with all the required steps shown

Let me know if you will have any question

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Problem set 1

May 29, 2020

Problem 1

If A, B and D are three events such that P (A ∪ B ∪ D) = 0.7, what is the value of

P (AC ∩ B C ∩ DC ) ?

Problem 2

Prove the following identity for any three events A, B and C:

P (A ∪ B ∪ D) = P (A) + P (B) + P (C) − P (A ∩ B) − P (A ∩ C) − P (B ∩ C) + P (A ∩ B ∩ C)

Problem 3

Suppose that the events A and B are disjoint. Under what conditions are AC and B C

disjoint?

Problem 4

Suppose that a committee of 12 people is selected in a random manner from a group of 100

people. Determine the probability that two particular people A and B will both be selected.

Problem 5

Consider an experiment in which a fair coin is tossed once and a balanced die is rolled once.

• Describe the sample space for this experiment.

• What is the probability that a head will be obtained on the coin and an odd number

will be obtained on the die?

Problem 6

Assuming that A and B are independent events, prove that the events AC and B C are also

independent.

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Problem set 1

May 29, 2020

Problem 7

Suppose that A, B, and C are three independent events such that P (A) = 1/4, P (B) = 1/3,

and P (C) = 1/2.

• Determine the probability that none of these three events will occur.

• Determine the probability that exactly one of these three events will occur.

Problem 8

A box contains five coins with a head on each side, three coins with a tail on each side, and

three fair coins. If one of these eleven coins is selected at random and tossed once, what is

the probability that a head will be obtained?

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