Chapter 10 - Probability and Discrete Random Variables

Question 1

What is the rule regarding total probability associated with a sample space?

Answer 1

The total probability associated with a sample space is 1.

Question 2

What is the rule regarding two events that are mutually exclusive (they cannot both happen in one trial?

Answer 2

If A and B are mutually exclusive (they cannot both happen in one trial), P(A or B) = P(A) + P(B)

Question 3

What is P(A’) the equivalent of? (Not A)

Answer 3

Not A or P(A’) = 1 - P(A)

Question 4

What is the rule regarding two events that are independent (one outcome doesn’t affect the other)?

Answer 4

If A and B are independent (one outcome doesn’t affect the other), then P(A and B) = P(A) x P(B)

Question 5

What are the conditions for a binomial distribution?

Answer 5

Conditions for a binomial probability distribution:

• Two possible outcomes in each trial.
• Fixed number of trials.
• Independent trials.
• Identical trials (p is the same for each trial).

Question 6

What is the formula for finding the probability of x successes for a binomial distribution?

Answer 6

The formula for finding the probability of a binomial cumulative distribution is:

P(X = x) = ⁿCₓpˣ(1-p)ⁿ⁻ˣ where n is the number of trials, and p is the probability of success in any given trial and x is the number of successes.

Question 7

How is a Binomial Distribution modelled (in terms of its parameters?)

Answer 7