Answer to Question #201207 in Statistics and Probability for zain

Question

A company has purchased a plant that must be installed and commissioned in 7 to 10 days by a services firm. The following table shows the services firm’s probability assessment for the number of days required to install and commission the plants from past experiences. Number of days 2 5 6 7 8 Probability 0.09 0.25 0.31 0.26 0.09 Let A be the event “the plant will be installed and commissioned in more than 6 days,” and let B be the event “the machinery will be installed and commissioned in less than 7 days” a. Find the probability of event A. b. Find the probability of event B. c. Find the probability of the complement of event A. d. Find the probability of the intersection of events A and B. e. Find the probability of the union of events A and B.

Answer 1

a.

$$P(A)=0.26+0.09=0.35$$

b.

$$P(B)=1-0.35=0.65$$

c.

$$P(A')=1-P(A)=1-0.35=0.65$$

d.

$$P(A\cap B)=0$$

e.

$$P(A\cup B)=1$$