Question

plaintiff or the defendant. The outcome of the appeal, as well as the type of trial (judge or jury), was determined for each civil case. Suppose one of the 2,143 cases is selected at random and both the outcome of the appeal and the type of trial are observed Jury JudgeTotals Plaintiff trial win_ reversed Plaintiff trial win- affirmed/dismissed 429 240 669 Defendant trial win- reversed Defendant trial win- affirmed/ dismissed 731 299 1,030 Totals a. Find P(A), where A (jurytrial 194 7 265 111 68 179 1,465678 2,14:3 b. Find P(B), where B (plaintifftrialwinis reversed) c. Are A and B mutually exclusive events? d. Find P(Ac) e. Find P(A U B) f. Find P(A n B) 2. " Airless , paint spray guns do not need an external sourceof compressed air connected to he gun by a heavy hose (although they do need a cord to attach them to a power source) because they have incorporated a small electric motor and pump. One common design uses, an induction motor that does not cause sparking because it does not require a com mutator and brushes (which are sources of sparking). Nevertheless the gun carries a label warning users that électrical devices operated in paint spray environments pose special dangers. Another type of gun that, like the first, also requires only a power cord is designed to weigh less by using a high-speed universal motor and a disk-type pump. The universal motor does require a commutator and brushes, which cause sparking. This second kind of spray gun carries a warning similar to that attached to the first, but it states in addition that the gun should never be used with paints that employ highly volatile and flammable thin- ners such as naphtha. The instruction booklet is quite detailed in its warnings. A painter had been lent one of the latter types of spray guns. In order to clean the apparatus, he partially filled it with paint thinner and operated it. It caught fire, and the painter was severely burned as the fire spread. The instruction booklet was in the card- board box in which the gun was kept, but it had not been read by the painter, who was a recent immigrant and did not read English very well. He had, however, used the first type of airless paint spray gun in a similar manner without mishap. The warning mes sages on both guns looked pretty much the same. Do you see any ethical problems in continuing over-the-counter sales of this second type of spray gun? What should the manufacturer of this novel, lightweight device do? In answering these questions, consider the fact that courts have ruled that hidden design defects are not excused by warnings attached to the defective products or posted in salesrooms. Informed consent must rest on a more thorough understanding than can transmitted to buyers by warning labels.

Answer 1

dear student, please post the question one at a time.

a) $P(A)=P(jurytrials)=\frac{1465}{2143}=0.6836$

b) $P(B)=\frac{265}{2143}=0.1237$

c) Two events are mutually exclusive if they cannot both occur at the same time.

i.e $P(A\cap B)=0$

Hence A and B are not mutually exclusive as $P(A\cap B)=\frac{194}{2143}=0.0905$

d) $P(A^c)=1-P(A)=1-0.6836=0.3164$

e) $P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.6836+0.1237-0.0905=0.7168$

f) $P(A\cap B)=0.0905$