# Finding Probability with Given Restrictions

12. Let E, F, and G be three events. Find expressions for the events so that of E, F, and G:

(a) only E occurs;

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

(c) at least one of the events occurs;

(d) at least two of the events occur;

(e) all three occur;

(f) none of the events occurs.

https://brainmass.com/math/probability/finding-probability-with-given-restrictions-32754

#### Solution Preview

Let the events E, F and G be independent of each other

Let the probability of occurrence of E be denoted by P(E)

Then the probability of E not occurring = Q(E) = {1-P(E)}

Let the probability of occurrence of F be denoted by P(F)

Then the probability of F not occurring = Q(F) = {1-P(F)}

Let the probability of occurrence of G be denoted by P(G)

Then the probability of G not occurring = Q(G) = {1-P(G)}

a) Only E occurs;

This means that E occurs and F and G do not occur

Probability of E occurring and F and G not occurring =

P(E) x Q (F) x Q (G)

= P(E) x {1-P (F)} x {1-P (G) }

Answer: P(E) x {1-P (F)} x {1-P (G) }

b) Both E and G but ...

#### Solution Summary

The solution gives expressions for the probability of the events.