1) According to Internet security experts, approximately 90% of all email 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 email messages and checks to see whether or not each one is legitimate.

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 seventh message she checks.

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

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

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

2) This year, there are seven freshmen, ten sophomores, eight juniors, and seven seniors are eligible to be on a committee.

In how many ways can a dance committee of 8 students be chosen?

ways=

In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors.

ways=

In how many ways can a dance committee be chosen if it is to consist of 4 juniors and 4 senions.

ways=

Determine theprobabilityof selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors.

Answer:

Determine theprobabilityof selecting a committee consisting of 4 juniors and 4 seniors.

Answer: