Suppose that we have a sample space s = {e 1, e 2, e 3, e 4, e 5, e 6, e 7}, where e 1, e 2, e 7 denote the sample points. the following probability assignments apply: p(e 1) = 0.1, p(e 2) = 0.15, p(e 3) = 0.15, p(e 4) = 0.2, p(e 5) = 0.1, p(e 6) = 0.05, and p(e 7) = 0.25. a= {e1, e4, e6} b= {e2, e4, e7} c= {e2, e3, e5, e7} (a) find p(a), p(b), and p(c). (b) what is p(a ∩ b)? (c) what is p(a ∪ b)? (d) are events a and c mutually exclusive?

(a) The probability of P(A), P(B), and P(C) are 0.35, 0.6 and 0.65 respectively.

(b) The probability of P(A ∩ B) is 0.2.

(c) The probability of P(A ∪ B) is 0.75.

(d) Events A and C mutually exclusive because the intersection of set A and C is null set or ∅.

Step-by-step explanation:

The given sample space is

It is given that

(a)

Therefore the probability of P(A), P(B), and P(C) are 0.35, 0.6 and 0.65 respectively.

(b)

A ∩ B represent the common elements of set A and set B.

The probability of P(A ∩ B) is 0.2.

(c)

A ∪ B represent all the elements of set A and set B.

The probability of P(A ∪ B) is 0.75.

(d)

Set A and C has no common element. So, the intersection of set A and C is empty set.

Yes, events A and C mutually exclusive because the intersection of set A and C is null set or ∅.

its 4 because 2 times 2 is 4, if you double the number two you get four