ransactions 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 94% 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).

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wifilethbridge wifilethbridge · Answer 1 · 2019-09-16T07:25:23+02:00

Answer:

The probability that a transaction can be completed in less than 100 milliseconds if 30% of transactions are changes is 0.718

Step-by-step explanation:

Let A be the vent of new item

Let B be the event of transaction completed in less than 100 milliseconds

[tex]A^c = \text{change item}[/tex]

Since we are given that 30% of transactions are changes,

So, [tex]A^c =0.3[/tex]

We are given that The addition of an item can be completed less than 100 milliseconds 94% of the time

So, [tex]P(B|A)=0.94[/tex]

We are also given that only 20% of changes to a previous item can be completed in less than this time.

So,[tex]P(B|A^c)=0.2[/tex]

[tex]P(A)=1-P(A^c) = 1 - 0.3 = 0.7[/tex]

So, the probability that a transaction can be completed in less than 100 milliseconds :

= [tex]P(B|A) \times P(A) +P(B|A^c) \times P(A^c)[/tex]

= [tex]0.94 \times 0.7 +0.2 \times 0.3[/tex]

= [tex]0.718[/tex]

Hence the probability that a transaction can be completed in less than 100 milliseconds if 30% of transactions are changes is 0.718