A metropolitan school system consists of three school districts-norths, south, central. The north district contains 25% of all students, the south district contains 40%, and the central district contains 35%. A minimum-competency test was given to all students; 10% of the north district students failed, 15% of the south distri
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The oasis outpost of Abu Ilan, in the heart of the Negev desert, has a population of 20 Bedouin tribesmen and 20 Farima tribesmen. El Kamin, a nearby oasis, has a population of 32 Bedouins and 8 Farima. A lost Israeli soldier, accidentally separated from his army unit, is wandering through the desert and arrives at the edge of o
The problems are from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions. If there is anything unclear in the problem, please tell me. Thank you very much.
14. A parallel system functions whenever at least one of its components works. Consider a parallel system of n components and suppose that each component independently works with probability ½. Find the conditional probability that component 1 works given that the system is functioning.
Let Qn denote the probability that in n tosses of a fair coin no run of 3 consecutive heads appears. Show that: Qn = ½ Qn-1 + ¼Qn-2 + ⅛Qn-3 Q0 = Q1 = Q2 = 1 Find Q8. HINT: Condition of the first tail. Please see attached for proper equation format.
Do Problem 2 ONLY please. Problem 1 An urn contains n+m balls, of which n are red and m are black. They are withdrawn from the urn, one at a time and without replacement. Let X be the number of red balls removed before the first black ball is chosen. Find E[X]. To obtain this quantity, number the red balls from 1 to n. Now
Political prisoners Mathew, Mark, and Luke are told that two of the three are to be executed. Matthew takes the jailer aside and says, "We both know that at least one of the others, Mark or Luke, will be executed; if you know, tell me the name of one who will be executed." After mulling this request over, the jailer can see no
Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(A|B) = __________. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(B|A) = __________.
A jar contains black and white marbles. Two marbles are chosen without replacement. If the probability of selecting a black marble and a white marble is 0.34, and the probability of selecting a black marble on the first draw is 0.47, find the probability of selecting a white marble on the second draw, given that the first marble
For Statistics for Quality Control
In an experiment, subjects are required to generate a "yes" or "no" decision. The probability of 'Yes' being correct is 50%. The observed probability of yes decisions is 70%. What is the probability that any "Yes"-outcome question will be answered correctly? Illustrate computational details of answer briefly.