For three events EFand G state expressions for For three eve

For three events, E,F,and G, state expressions for...

For three events E, F and G, state expressions for... a.only E occurs b. both E and G but not F occurs c. at least one of the events occurs d. at least two of the events occur e. all three events occur f. none of the events occur g. at most one of the events occurs h. at most, two of the events occur i. exactly two of the events occur j. at most, three of the events occur.

Solution

Answer:

(a)only E occurs

P (E) = Probability that only event E will occur

(b)both E and G but not F, occur

P (E) * P (G) = Probability that E and G will occur but notevent F

(c)at least one of the events occurs

P (E) + P (F) + P (G) = Probability that either event E or eventF or event G will occur.

(d)at least two of the events occur

[P (E) * P (F)] + [P (E) * P (G)] + [P (F) * P (G)] + [P (E) * P(F) * P (G)] = Probability that at least two of the events willoccur, not less then two

(e)all three events occur

P (E) * P (F) * P (G) = Probability that all three events willoccur

(f) none of the events occur

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