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1). Consider a sample space of five outcomes A, B, C and D. Which of the following represent...

Question:

1). Consider a sample space of four outcomes A, B, C and D. Which of the following represent legitimate probability models? Circle all that are correct.

a). p(A) = 0.20,p(B) = 0.20,p(C) = 0.20,p(D) = 0.20

b). p(A) = 0.25,p(B) = 0.25,p(C) = 0.25,p(D) = 0.25

c). p(A) = 0.10,p(B) = 0.20,p(C) = 0.30,p(D) = 0.30

d). p(A) = 0.40, p(B) = 0.40, p(C) = 0.30,p(D) = -0.10

2). Suppose an experiment has four possible outcomes - A, B, C and D. If the probability of A occurring is 0.22, of B occurring, is 0.31 and of C occurring is 0.40, what is the probability that D occurs? Explain your reasoning.

Answer and Explanation:

1). Consider a sample space of four outcomes A, B, C and D. Which of the following represent legitimate probability models? Circle all that are correct.

a). p(A) = 0.20,p(B) = 0.20,p(C) = 0.20,p(D) = 0.20

The sum is p(A) + p(B) + p(C) + p(D) = 0.8.

Therefore this is not a valid model.

b). p(A) = 0.25,p(B) = 0.25,p(C) = 0.25,p(D) = 0.25

The sum is p(A) + p(B) + p(C) + p(D) = 1.

Therefore this is a valid model.

c). p(A) = 0.10,p(B) = 0.20,p(C) = 0.30,p(D) = 0.30

The sum is p(A) + p(B) + p(C) + p(D) = 0.9.

Therefore this is not a valid model.

d). p(A) = 0.40, p(B) = 0.40, p(C) = 0.30,p(D) = -0.10

The sum is p(A) + p(B) + p(C) + p(D) = 1 but one of the probabilities is negative.

Therefore this is not a valid model.

2). Suppose an experiment has four possible outcomes - A, B, C and D. If the probability of A occurring is 0.22, of B occurring, is 0.31 and of C occurring is 0.40, what is the probability that D occurs? Explain your reasoning.

The sum of all 4 probabilities must be 1, thus,

P(D) = 1 - P(A) - P(B) - P(C) = 1 - 0.22 - 0.31 - 0.4 = 0.07


Learn more about this topic:

What is Probability in Math? - Definition & Overview

from High School Algebra I: Help and Review

Chapter 24 / Lesson 7
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