Question

According to Internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while the remaining 10% are legitimate. A system administrator wishes to see if the same percentages hold true for the e-mail traffic on her servers. She randomly selects e-mail messages and checks to see whether or not each one is legitimate. (Unless otherwise specified, round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)

Assuming that 90% of the messages on these servers are also spam, compute the probability that the first legitimate e-mail she finds is the fifth message she checks.

Compute the probability that the first legitimate e-mail she finds is the fifth or sixth message she checks.

Compute the probability that the first legitimate e-mail she finds is among the first five messages she checks.

On average, how many messages should she expect to check before she finds a legitimate e-mail? (Round your answer to one decimal place.)

Answer 1

1)

probability that the first legitimate e-mail she finds is the fifth message she checks =

0.9*0.9*0.9*0.9*0.1

=0.0656

2)

probability that the first legitimate e-mail she finds is the fifth or sixth message she checks =

0.9*0.9*0.9*0.9*0.1+0.9*0.9*0.9*0.9*0.9*0.1

=0.1247

3)

probability that the first legitimate e-mail she finds is among the first five messages she checks =

1 - probability that the no legitimate e-mail she finds among the first five messages she checks

= 1- 0.9*0.9*0.9*0.9*0.9

= 1 - 0.5905

= 0.4095

4)

On average, how many messages should she expect to check before she finds a legitimate e-mail

= 10

Thanks in advance!

revert back for doubt

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