Which of the following probabilities for the sample points A

Which of the following probabilities for the sample points A, B, and C could be true if A, B, and C are the only sample points in an experiment?   Explain why each of the other 3 options are not true

. A) P(A) = 1/10, P(B) = 1/10, P(C) = 1/10

B) P(A) = 1/2, P(B) = 1/7, P(C) = 1/8

C) P(A) = -1/4, P(B) = 1/2, P(C) = 3/4

D) P(A) = 0, P(B) = 1/8, P(C) = 7/8

Solution

AS YOU KNOW THE SUM OF ALL PROBABILITIES IN AN EXPERIMENT ALWAYS IS 1

lets see

a)

1/10 + 1/10 + 1/10 = 3/10

this is wrong because the sum is not 1

b)

1/2 + 1/7 + 1/8 = 0.7678

the same mistake, need to be 1 always

c)

P(A) = -1/4

the probabilities always are positive, there are never negative probabilities

d)

1/8 + 7/8 = 1

this is the true