A fair die is rolled five times calculate the probability

Question

1) Use the formula C(n, x)p^xq^{n - x}to determine the probability of the given event. (Round your answer to four decimal places.)

The probability of no  success in nine trials of a binomial experiment in which p= 1/4.

2)Use the formula C(n, x)p^xq^{n - x}to determine the probability of the given event. (Round your answer to four decimal places.)

The probability of at least on failure in six trials of a binomial experiment in which p=1/4

3) A fair die is rolled five times. Calculate the probability of obtaining exactly two 1s. (Round your answer to four decimal places.)

4) A psychology quiz consists of ten true-or-false questions. If a student knows the correct answer to six of the questions but determines the answers to the remaining questions by flipping a coin, what is the probability that she will obtain a score of at least 90%.  (Round your answer to three decimal places.

5) The probability that a DVD player produced by VCA Television is defective is estimated to be 0.08. A sample of ten players is selected at random. (Round your answers to four decimal places.)

(a) What is the probability that the sample contains no defective units?

(b) What is the probability that the sample at most contains two defective units?