Math Answers

 Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. During a given hour, what are the probabilities that

(a) no more than three customers arrive?

(b) at least two customers arrive?

(c) exactly four customers arrive? 

A salesperson has found that the probability of a sale on a single contact is approximately .03. If the salesperson contacts 100 prospects, what is the approximate probability of making at least one sale?

A shipment of 20 cameras includes 3 that are defective. What is the minimum number of cameras that must be selected if we require that P(at least 1 defective)≥ .8?

A warehouse contains ten printing machines, four of which are defective. A company selects five of the machines at random, thinking all are in working condition. What is the probability that all five of the machines are nondefective?

An urn contains ten marbles, of which five are green, two are blue, and three are red. Three marbles are to be drawn from the urn, one at a time without replacement. What is the probability that all three marbles drawn will be green?

Given that we have already tossed a balanced coin ten times and obtained zero heads, what is the probability that we must toss it at least two more times to obtain the first head?

An oil prospector will drill a succession of holes in a given area to find a productive well. The probability that he is successful on a given trial is .2.

(a) What is the probability that the third hole drilled is the first to yield a productive well?

(b) If the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?

Ten motors are packaged for sale in a certain warehouse. The motors sell for $100 each, but a double-your-money-back guarantee is in effect for any defectives the purchaser may receive. Find the expected net gain for the seller if the probability of any one motor being defective is .08. (Assume that the quality of any one motor is independent of that of the others.)

A missile protection system consists of n radar sets operating independently, each with a probability of .9 of detecting a missile entering a zone that is covered by all of the units.

(a) If n = 5 and a missile enters the zone, what is the probability that exactly four sets detect the missile? At least one set?

(b) How large must n be if we require that the probability of detecting a missile that enters the zone be .999?

A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identical components, each with a probability of .2 of failing in less than 1000 hours. The subsystem will operate if any two of the four components are operating. Assume that the components operate independently. Find the probability that;

(a) Exactly two of the four components last longer than 1000 hours.

(b) The subsystem operates longer than 1000 hours.