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

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 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.