Question

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 1

There is a 62.7% probability that a transaction can be completed in less than 100 milliseconds.

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 milliseconds

The probability P that a transaction can be completed in less than 100 milliseconds is:

`P = P_(1) + P_(2)`

In which
`P_(1)` is the probability that the transaction is an addition and it takes less than 100 milliseconds. So

`P_(1) = 0.7*0.81 = 0.567`

`P_(2)` is the probability that the transaction is a change and it takes less than 100 milliseconds. So

`P_(2) = 0.2*0.3 = 0.06`

So

`P = P_(1) + P_(2) = 0.567 + 0.06 = 0.627`

There is a 62.7% probability that a transaction can be completed in less than 100 milliseconds.