Transactions to a computer database are either new items or changes to previous items. The addition of an item can be completed less than 100 milliseconds 81% of the time, but only 20% of changes to a previous item can be completed in less than this time. If 30% of transactions are changes, what is the probability that a transaction can be completed in less than 100 milliseconds? Round your answer to two decimal places (e.g. 98.76).

Answer:There is a 62.7% probability that a transaction can be completed in less than 100 milliseconds.Step-by-step explanation:This a probability problem.We have the following probabilities:-70% probability that a transaction is an addition of an item.-30% probability that a transaction is a change to an item-81% probability that an addition can be completed in less than 100 milliseconds-20% probability that change can be completed in less than 100 millisecondsThe probability P that a transaction can be completed in less than 100 milliseconds is:[tex]P = P_{1} + P_{2}[/tex]In which [tex]P_{1}[/tex] is the probability that the transaction is an addition and it takes less than 100 milliseconds. So[tex]P_{1} = 0.7*0.81 = 0.567[/tex][tex]P_{2}[/tex] is the probability that the transaction is a change and it takes less than 100 milliseconds. So[tex]P_{2} = 0.2*0.3 = 0.06[/tex]So[tex]P = P_{1} + P_{2} = 0.567 + 0.06 = 0.627[/tex]There is a 62.7% probability that a transaction can be completed in less than 100 milliseconds.