1. What is the probability that three dice thrown simultaneously land on the same face (i.e. three "1"s OR three "2s"...etc... OR three "6s")?

2. You randomly draw three balls from a large bag that contains 600 white balls and 400 red balls. Assuming that the proportion of balls of each color does not vary during a draw:

a) Give a reason why the Poisson distribution is not well suited to calculate probabilities in such a draw b) Calculate the probability that the first ball is white c) Calculate the probability of getting 2 white balls and a red ball

3. You need to test a new shipment of crates of peanuts for contamination with certain strains of Aspergillus, which produce aflatoxin, a carcinogen. Your historical data suggests an average rate of 2% (po = 0.02) of contaminated peanuts in the case of contaminated lots (note: these are fictitious data for review purposes). You decide to analyze 200 peanuts chosen at random from this batch, which we will assume to be contaminated.

a) What number of contaminated peanuts can you expect to find on average? b) What is the probability of observing this mean result?

c) What is the probability of not detecting Aspergillus contamination (finding zero contaminated peanuts)?

4. A random sample of 20 observations from a normal population, with known standard deviation equal to 8, gives a mean of 40.

a) Calculate the confidence limits for a confidence level corresponding to a significance factor = 5% b) Calculate the probability of 0.22 < Z < 1.63

5. We have a sample with n = 20, s = 14 and x = 70. Calculate IC95%.