Imagine rolling a fair six-sided die four times. a. What is the theoretical probability that all four rolls of the die show a 5 on top? b. What is the theoretical probability the first roll of the die shows a 2 and the next three rolls show a 5 on top? a. P(all four rolls are 5) = (Type an integer or a simplified fraction.) b. P(first toss is 2 and rest are 5) = (Type an integer or a simplified fraction.)

A club has a membership of 6 freshmen, 2 sophomores, 3 juniors and 4 seniors.  A committee of 4 is chosen.  Find each as a fraction or a decimal rounded to 2 decimal places. a.  What is the probability that the committee consists of all freshmen?  b.  What is the probability that the committee consists of 2 juniors and 2 seniors? c.  What is the probability that the committee consists of all sophomores?

A. If 6% of the population of grass in Kentucky is bluegrass, find the probability that in a sample of 150 acres, there are exactly 6 acres of Kentucky bluegrass. B. Find the probability that there are at most 2 acres of Kentucky bluegrass.

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