Question # 4 An inspection procedure at a manufacturing plant involves picking t

Question

Question # 4 An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least two of the three items are in perfect condition, if in reality 92% of the whole lot is perfect, what is the probability that the lot will be accepted? Question # 5 Suppose the among the 6000 students in a school district, 1500 are taking honors course and 1800 prefer watching basketball to watching football. If taking honors courses and preferring basketball are independent, how many students are both taking honors courses and prefer basketball to football? Question #6 Suppose that, in a certain part of the world, in any 50-year period the probability of a major plague is .28, the probability of a major famine is .57, and the probability of both a plague and a famine is.18. What is the probability of a famine given that there is a plaque? What is the probability that neither a famine nor a major plaque will happen? Are the events independent? Are the events mutually exclusive? Question #7 IF P(A) -0.2 and P(B) -0.1, What is the P[A or B) if A and B are independent and not mutually exclusive?

Explanation / Answer

Q4) This is a question of binomial theorm where we have probability of success p=0.92 and the probability of failure q=1-p = 1-0.92 =0.08

So writing the equation

P(X=x) = nCx * p^x * q^(n-x)

Now the inspector will pick 3 balls and if minimum 2 out of 3 are perfect then he will accept the lot and so the probability of acceptance is for x=2,3

P(X=2) +P(X=3) = 3C2 * 0.92^2 * 0.08^1 + 3C3 * 0.92^3 * 0.08^0

=0.981824

So ., 0.981824 is the probability that the whole lot will be selected.

As per the chegg policy we are supposed to answer 1 full question only at a time. If you want the ans for the rest please post them seperately. Hope you understand.

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---