A machine has a probability of producing a defective equal to 0.05 every time it produces a product. If three of its products are selected randomly and independently during a shift, what is the probability that a quality engineer will find no defectives in the three?

A machine can be in one of four states: ‘running smoothly’ (state 1), ‘running but needs adjustment’ (state 2), ‘temporarily broken’ (state 3), and ‘destroyed’ (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. ˆ If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. ˆ If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine to…

solve question 6 pleaseee

A stock index consists of businesses in both Europe and the United States. Assume that each business comprising the stock index makes a profit or loss independently of the other businesses in the index. Suppose that an American business on the stock index makes a profit 60%60% of the time and a European business makes a profit 80%80% of the time. If there are 840 American businesses and 720 European businesses in the stock index, what is the expected number of businesses in the stock index to make a profit?