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.

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.

...Find the probability that the spinner stops on the same ... What is the probability that the results are all heads or ... person that works at a company is given 1 5 ...

... 140 Standardizing the variable X using Z = = and from standard normal σ 50 tables, we can find the probabilities as follows ... a. Find the probability that an ...

... pre employment drug tests on the job applicants who were to engaged in safety related jobs and found that 1143 ... The probability that a given alternator will ...

... The probability is _____. Answer. ... Let B be the event that the kid has sore throat. Given, P (A) = 90% = 0.9 P (B/A) = 20% = 0.2 We want to find P (kid who ...

... yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean u ...

... selected randomly from the manufacturing output, what is the probability that ... and from standard normal σ 1 tables, we can find the probabilities as follows ...

... Bayes uses past and prior probabilities for updates while Shafer-Dempster ... The binomial distribution is appropriate to use to find the probability of the ...

... The reasons cited for finding that the town did not have a ... (3) The absolute freedom given in the ... would have continued, there is a great probability that all. ...

... c. the joint probabilities must total less than 1. d ... 35. Find the shortest route from Node 1 to Node 5 ... distribution has been developed, and the probability of 2 ...

... is based on r2, using the given formula to ... Number Range Interval Occurrences P(x) Probability (days) 1.0 4 ... based on its distribution, to find the distribution ...