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3 years ago

Consider a sample space of three outcomes A,B,and C. Which of the following represent legitimate probability models?

Mathematics

2 answers:

NeX [460]3 years ago

8 0

Answer B & C are correct because P(A) + P(B) + P(C) add up to 1

Karolina [17]3 years ago

7 0

Answer:

B. P(A)=0.2, P(B)=0.1, P(C)=0.7

E. P(A)=0.3, P(B)=0.3, P(C)=0.4

Step-by-step explanation:

A fundamental property of probability is that the sum of the probabilities of the events is equal to 1.

Another property is that the probability of any event must be greater than or equal to zero, it can never be a negative value.

Case A. P(A)=0.1, P(B)=0.1, P(C)=1

P(A) + P(B) + P(C) = 0.1 + 0.1 + 1 = 1.2 ≠ 1 (It is not a legitimate probability model)

Case B. P(A)=0.2, P(B)=0.1, P(C)=0.7

P(A) + P(B) + P(C) = 0.2 + 0.1 + 0.7 = 1 (It is a legitimate probability model)

Case C. P(A)=-0.4, P(B)=0.9, P(C)=0.5

P(B) = -0.4 is a negative value (It is not a legitimate probability model)

Case D. P(A)=0.5, P(B)=0,P(C)=0.4

P(A) + P(B) + P(C) = 0.5 + 0 + 0.4 = 0.9 ≠ 1 (It is not a legitimate probability model)

Case E. P(A)=0.3, P(B)=0.3, P(C)=0.4

P(A) + P(B) + P(C) = 0.3 + 0.3 + 0.4 = 1 (It is a legitimate probability model)

Hope this helps!

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