1. Suppose that two trucks, truck 1 and truck 2, in a factory are operated indep

Question

1. Suppose that two trucks, truck 1 and truck 2, in a factory are operated independently of each other. Let A be the event that truck 1 will become inoperative during a given 8-hour period, let B be the event that truck 2 will become inoperative during the same period, and suppose that P(A) = 1/3 and P(B) = 1/4. What is the probability that at least one of the truck will become inoperative during the given period?

2. Max is hired to grade a multiple choice exam. The probability that he will make a grading error on any given question of this exam is .1.

(a) If there are ten questions and questions are graded independently, what is the probability that no errors are made?

(b) If there are n questions, questions are graded independently, and the probability of a grading error is p (instead of .1), what is the probability that no errors are made?

Explanation / Answer

1. Since trucks are inoperative independently so

P(A and B) =P(A)P(B) = (1/3) (1/4) = 1/12

So the probability that at least one of the truck will become inoperative during the given period is

P(A or B) = P(A) + P(B) - P(A)P(B) = (1 / 3)+(1/4)-(1/12)= 6/12 = 1/2

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.