A university class has 20 students: 10 are accounting majors, 3 are psychology majors, and 7 are nursing majors. (Each student has only one of these majors.) The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that two psychology majors will be selected? Do not round your intermediate computations. Round your final answer to three decimal places. (If necessary, consult a list of formulas.)

Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, three green ones, two white ones, and two purple ones. She grabs seven of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She has at most one green one.

Robby wins 2 out of every 3 chess matches he plays with Marlene. What is the probability that he wins exactly 5 of the next 6 matches

Charles has six songs on a playlist. Each song is by a different artist. The artists are Joey McIntyre, Whitney Houston, Aaron Carter, Shakira, Shania Twain, and Phil Collins. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Aaron Carter and the second song is by Joey McIntyre? Write your answer as a fraction or a decimal, rounded to four decimal places.   The probability that the first song is by Aaron Carter and the second song is by Joey McIntyre is    .

If you have a sample of 100 patients at a hospital and 20 of them have the flu, what is the probability Of randomly selecting 3 patients in a row who have the flue?