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Interest centers around the nature of an oven purchased at a particular department store. It can be either a gas or electric oven. Consider the decision made by six distinct customers. (a) Suppose that the probability is 0.40 that at most, two of these individuals purchase an electric oven. What is the probability that at least three purchase the electric oven? (b) Suppose it is known that the probability that all six purchase the electric oven is 0.007 while 0.104 is the probability that all six purchase the gas oven. What is the probability that at least one of each type is purchased?

It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry as well as other areas in which the product is used in the home, for example, detergent. These machines are not perfect, and, indeed they may \(A,\) fill to specification, \(B,\) underfill, and \(C\), overfill. Generally, the practice of underfilling is that which one hopes to avoid. Let \(P(B)=0.001\) while \(P(A)=0.990\) (a) Give \(P\\{C)\). (b) What is the probability that the machine does not underfill? (c) What is the probability that the machine either overfills or underfills?

If \(R\) is the event that a convict committed armed robbery and \(D\) is the event that the convict pushed dope, state in words what probabilities are expressed by (a) \(P(R \backslash D)\) (b) \(P\left(D^{\prime} T R\right)\) (c) \(P\left(R^{\prime} \mid D^{\prime}\right)\)

A manufacturer of a flu vaccine is concerned about the quality of its flu serum. Batches of serum are processed by three different departments having rejection rates of \(0.10,0.08,\) and \(0.12,\) respectively. The inspections by the three departments are sequential and independent. (a) What is the probability that a batch of serum survives the first departmental inspection but is rejected by the second department? (b) What is the probability that a batch of serum is rejected by the third department?

The probability that an automobile being filled with gasoline will also need an oil change is 0.25 ; the probability that it needs a new oil filter is 0.40 ; and the probability that both the oil and filter need changing is 0.14 (a) If the oil had to be changed, what is the probability that a new oil filter is needed? (b) If a new oil filter is needed, what is the probability that the oil has to be changed?

The probability that a married man watches a certain television show is 0.4 and the probability that a married woman watches the show is \(0.5 .\) The probability that a man watches the show, given that his wife does, is 0.7 . Find the probability that (a) a married couple watches the show; (b) a wife watches the show given that her husband does; (c) at least 1 person of a married couple will watch the show.

For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21 , the probability that his wife will vote in the referendum is \(0.28,\) and the probability that both the husband and wife will vote is \(0.15 .\) What is the probability that (a) at least one member of a married couple will vote? (b) a wife will vote, given that her husband will vote? (c) a husband will vote, given that his wife does not vote?

The probability that a vehicle entering the Luray Caverns has Canadian license plates is \(0.12 ;\) the probability that it is a camper is 0.28 ; and the probability that it is a camper with Canadian license plates is \(0.09 .\) What is the probability that (a) a camper entering the Luray Caverns has Canadian license plates? (b) a vehicle with Canadian license plates entering the Luray Caverns is a camper? (c) a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper?

The probability that the head of a household is home when a telemarketing representative calls is 0.4 . Given that the head of the house is home, the probability that goods will be bought from the company is 0.3. Find the probability that the head of the house is home and goods being bought from the company.

The probability that a doctor correctly diagnoses a particular illness is 0.7 . Given that the doctor makes an incorrect diagnosis, the probability that the patient enters a law suit is 0.9 . What is the probability that the doctor makes an incorrect diagnosis and the patient sues?