Ch. 5 Conditional Probability

# Ch. 5 Conditional Probability - 1 PHIL 111 Inductive Logic...

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1 PHIL 111: Inductive Logic Fall 2009 Class Problems Chapter 5 (Conditional Probability) Pr(A/B) = Pr(A B)/Pr(B) 1 . Imagine two urns, each containing red and green balls. Urn A has 80% red balls, 20% green balls, and Urn B has 60% green, 40% red. You pick an urn at random (50%). [Make sure you draw a tree diagram and you complete the probability notation.] Let A = You rolled heads and you draw from Urn A Let B = You rolled tails and you draw from Urn B Let R = The random ball is red. Let G = The random ball is green. Pr(R/A) = 0.8 Pr (G/A) = .2 Pr(R/B) = 0.4 Pr (G/B) = .6 Pr(A) = Pr(B) = 0.5 a. Write the English translations for the probabilities in symbolic form using the letters given above: (1) Pr(R/A) (2) Pr(A/R) (3) Pr((R A) v (R B)) b. What is the probability of drawing a red? [Pr (R)] c. What is the probability of not drawing a red ball? Pr ( R) d. What is the probability of drawing a red given that you draw from Urn A? [Pr (R/A)] e. What is the probability that you drew from Urn A given that you drew a red ball? [Pr (A/R)] f. What is the probability that you drew from Urn B given that you drew a green ball? [Pr (B/G)] 2 . Imagine an automobile plant contracted to buy shock absorbers from two local suppliers, Bolt & Co. and Acme Inc. Acme supplies 60% and Bolt 40%. All Shocks are subject to quality control. Of Acme’s shocks, 96% test reliable. But Bolt has been having some problems on the line, and recently only 72% of Bolt’s shock absorbers have tested reliable. Let A = The shock Chosen at random was made by Acme. Let B = The shock Chosen at random was made by Bolt. Let R = The shock Chosen at random is reliable Pr(A) = 0.6 Pr(R/A) = 0.96 Pr(R A) = 0.576 Pr(B) = 0.4 Pr(R/B)= 0.72 Pr(R B) = 0.288 Pr(R) = Pr(R A) v Pr(R B) a. What is the probability that a randomly chosen shock absorber will test reliable? b. What is the probability that a shock absorber is made by Bolt, on the condition that it tested reliable? c. What is the probability that a shock absorber will not test reliable? d. What is the probability that a shock absorber is made by Bolt given that it tested not reliable? 3 . Imagine that Calgon has enrolled as a freshman at an Eastern university and the probability that he will get a scholarship is .35. If he gets a scholarship the probability that he will graduate is .82, and if he does not get a scholarship the probability that he will graduate is only .44.

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