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Probability and Combinatorics Problems, Exams of Mathematics

Drexel UniversityMathematics

A series of probability and combinatorics problems, including calculating the number of ways people can be seated in a room, finding arrangements of letters, determining probabilities of events, and analyzing the effectiveness of a new drug. Students studying statistics, probability, or combinatorics may find this document useful for exam preparation, assignments, or as study notes.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

koofers-user-2rg
koofers-user-2rg 🇺🇸

10 documents

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bg1
1. If 6 people enter a room with 14 chairs, in how many ways can they be seated?
(5 points)
2. Find the number of arrangements that can be formed from the letters in
ALABAMA.
(5 points)
3. Let A and B be two events in a sample space S such that P(A) = 0.4,
P(A|B) = 0.5, and P(AC BC) = 0.9
(10 points)
a) Find P(B)
b) Find P(B|A)
pf3
pf4

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Download Probability and Combinatorics Problems and more Exams Mathematics in PDF only on Docsity!

  1. If 6 people enter a room with 14 chairs, in how many ways can they be seated? (5 points)
  2. Find the number of arrangements that can be formed from the letters in ALABAMA. (5 points)
  3. Let A and B be two events in a sample space S such that P(A) = 0.4, P(A|B) = 0.5, and P(AC^  BC) = 0. (10 points) a) Find P(B) b) Find P(B|A)
  1. A medical center is testing the effectiveness of a new headache drug. A study is done with 1000 people with frequent headaches. 600 receive the actual drug and 400 are given a placebo. Of the people taking the drug, 65% claim the drug works. Of the people taking the placebo, 58% claim the drug works. Given that a randomly selected person claims the drug works, what’s the probability (s)he is actually taking the drug? (10 points)
  2. 30% of a company’s washing machines need repair after 1 year and 10% of the company’s drying machines need repair after 1 year. A person purchases both a washer and dryer from this company. What’s the probability (10 points) a) neither machine needs repair after 1 year? b) exactly 1 machine needs repair after 1 year?
  1. The probability of a random variable X is shown in the table (10 points) x P(X = x) -3 0. -2 0. -1 0. 0 0. 1 0. 2 0. 3 0. a) Draw the histogram b) Find P(X < 0) c) Find P(0 < X < 2) d) Find E(X) e) Find standard deviation