Question

Transactions to a computer database are either new items or changes to previous items. the addition of an item can be completed in less than 100 milliseconds 90% 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? (question 2-176) (put solution in the form 0.xx)

Answer 1

P(<100) = P((new or change) & <100) = P(new & <100) + P(change & <100)

... = P(<100 | new)*P(new) + P(<100 | change)*P(change)

... = 0.90*0.70 + 0.20*0.30

... = 0.63 + 0.06 = 0.69 . . . . probability of completing a transaction in < 100 ms