The accompanying Venn diagram illustrates a sample space containing six sample points and three events, A, B, and C. The probabilities of the sample points are P(1) = 0.3, P(2) = 0.2, P(3) = 0.1, P(4) = 0.1, P(5) = 0.1 and P(6) = 0.2.
Find:

Step-by-step explanation:

To find the probability of a certain set, we must add the probability of the points that are contained in the specific set.

a) P(A): Add the probability of 1,3,5. That is P(1)+P(3)+P(5) = 0.5

b) . This set has no points in it, so its probability is 0.

c) P(A\cup B \cup C): Add the probability of 1,2,3,4,5,6. So, it is 1.

d) . P(C)  is the probability by summing 5,6,2 so P(C) = 0.5. So

e) That is, all the points that are in A but not in C. So add 1,3. Then the probability is 0.4

e'), using the definition of conditional probabily and results a,b.

f) Two events are mutually exlusive if the probability of their intersection is 0. In this case A and C are not mutually exclusive, since is the probability of 5, that is 0.1. Since 0.1>0, they are not mutually exclusive.

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