Dice probability of a sum of 5 , math homework help

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A multiple choice test consists of eight questions, each of which has five choices. Each question has exactly one correct answer.
William guesses randomly at each answer. What is the probability that he gets six or fewer questions correct? (Round your answer to four decimal places.)
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In a class of 19 students, 5 are math majors. A group of four students is chosen at random. (Round your answers to four decimal places.)
(a) What is the probability that the group has no math majors?
(b) What is the probability that the group has at least one math major?
(c) What is the probability that the group has exactly two math majors?
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If you roll two four-sided dice (numbered 1, 2, 3, and 4), what is the probability that the sum of the dice is 5?
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Illinois license plates used to consist of either three letters followed by three digits or two letters followed by four digits. Assume that all the different possible license plates
are equally likely.
(a) What is the probability that a randomly chosen plate contains the number 5555? (Round your answer to six decimal places.)
(b) What is the probability that a randomly chosen plate contains the substring HI? (For example, H14321 or PHI786 are two ways HI might appear. Round your
answer to six decimal places.)
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An urn contains two red balls and five blue balls.
Draw four balls at random from the urn, without replacement. Compute the expected number of red balls in your sample. (Round your answer to four decimal places.)