Consider a sample space of three outcomes a, b,and c. which of the following represent legitimate probability models?
a. p(a)=0.1, p(b)=0.1, p(c)=1
b. p(a)=0.2, p(b)=0.1, p(c)=0.7
c. p(a)=-0.4, p(b)=0.9, p(c)=0.5
d. p(a)=0.5, p(b)=0,p(c)=0.4
e. p(a)=0.3, p(b)=0.3, p(c)=0.4

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!

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1

it is not that hard all u have to do is plot the graph

step-by-step explanation: