On a rainy day an unnamed statistics professor decides to play with an urn containing

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On a rainy day an unnamed statistics professor decides to play with an urn containing bottle caps. Five were from Guinness, ten Bass, and ten Smithwicks. He picks a cap at random, looks at it, and then replaces it in his urn. He does this eight times because he is very bored.

1. What is the probability that he will pick a Guinness every time?

2. What is the probability that he will pick a Guinness exactly seven times?

3. What is the probability that he will pick something other than a Guinness exactly once?

4. What is the probability that he will pick a Guinness at most six times?

5. What is the probability that he will pick something other than a Guinness at least twice?

6. What is the mean number of Guinness caps he should see in eight trials?

7. What is the standard deviation for the number of Guinness caps appearing in eight trials?