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# Interpretations of Probability

1) The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2 respectively. Let A denote the event {a, b, c} and B denote the event {c, d, e}. Determine the following:

a) P(A)
b) P(B)
c) P(A')
d) P(A U B)
e) P(A n B)

2) If the last digit of a weight measurement is equally likely to be any of the digits 0 through 9, what is the probability that the lat digit is 0? What is the probability that the last digit is greater than or equal to 5?

3) An injection-molded part is equally likely to be obtained from any of the eight cavities on a mold.

a) What is the sample space?
b) What is the probability a part is from cavity 1 or 2?
c) What is the probability that a part is from neither cavity 3 nor 4?

4) In a NiCd battery, a fully charged cell is composed of nickel, an element that has multiple oxidation states. It is usually found in the following states:
[see attachment]

a) What is the probability that a cell has at least one of the positive nickel charged options?
b) What is the probability that a cell is not composed of a positive nickel charge greater than +3?

5) Suppose your vehicle can have a license plate that consists of three digits (0 - 9) followed by three letters (A - Z). IF a license plate is selected randomly, what is the probability that yours is the one selected?

#### Solution Preview

a) P(A)

This is the probability of choosing either a, b, or c (since these are in A). The probability of choosing a, b, or c is 0.1 + 0.1 + 0.2 = 0.4.

The answer is P(A) = 0.4.

b) P(B)

This is the probability of choosing either c, d, or e (since these are in B). The probability of choosing c, d, or e is 0.2 + 0.4 + 0.2 = 0.8.

The answer is P(B) = 0.8.

c) P(A')

This is the probability of choosing something not in A. You could find it either by subtracting P(A) from 1 (1 - P(A) = 1 - 0.4 = 0.6), or by adding together the probabilities of choosing d and e (since they are not in A; 0.4 + 0.2 = 0.6).

The answer is P(A') = 0.6.

d) P(A U B)

This is the probability of choosing something that ...

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