A commuter passes through two traffic lights on the way to work. Each light is r

Question

A commuter passes through two traffic lights on the way to work. Each light is red, yellow, or green. An experiment consists of observing the colors of the two lights. List the 9 outcomes in the sample space. Let A be the event that both colors are the same. List the outcomes in A. Let B be the event that the two colors are different. List the outcomes in B. Let C be the event that at least one of the lights is green. List the outcomes in C. Are events A and B disjoint? Explain. Are events A and C disjoint? Explain. Compute P (A) (Given fraction) Compute P (A or B) (Given fraction) Compute P (B or C) (Given fraction)

Explanation / Answer

f) No, A and C are not disjoint because outcome GG is common in both A and C.

g) P(A)

= (Number of outcomes in A)/ (Total number of outcomes)

= 3/ 9

= 1/3

h) P(A or B) = P(A) + P(B) - P(A and B)

Since A and B are disjoint, P(A and B) = 0

So,

P(A or B)

= P(A) + P(B)

= 3/9 + 6/9

= 9/9

= 1

i) P(B or C) = P(B) + P(C) - P(B and C)

We can see that there are 4 outcomes which are common in B and C. So,

P(B and C) = 4/9

Hence,

P(B or C)

= 6/9 + 5/9 - 4/9

= 7/9

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