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Bayes Theorem. Make a tree: $P(L) = 0.0365$ and $P(A \textrm{ and } L) = (0.4)(0.05) = 0.02$, so P(shipped from A given that the computer is late) = 0.548, approximately.
Exercise 1. A doctor is called to see a sick child. The doctor has prior information that 90% of sick children in that neighborhood have the u, while the other 10% are sick with 1
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SECTION 9.2 PROBLEM SET: BAYES' FORMULA Jar I contains five red and three white marbles, and Jar II contains four red and two white marbles. A jar is picked at random and a marble is drawn.
Example problems. Click on the problems to reveal the solution. Problem 1. Consider a test to detect a disease that 0.1 % of the population have. The test is 99 % effective in detecting an infected person. However, the test gives a false positive result in 0.5 % of cases.
The example on Bayes' Theorem in Section 1.2 concerning the biology of twins was based on the assumption that births of boys and girls occur equally frequently, and yet it has been known for a very long time that fewer girls are born than boys (cf. Arbuthnot, 1710). Suppose that the probability of a girl is p, so that. P(GGjM) = p; P(GGjD) = p2;
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This section contains a number of example problems solved using Bayes theorem, and commentary about the problem. The standard solution process is used to solve each problem.
TOTAL PROBABILITY AND BAYES THEOREM Example 1 A biased coin (with probability of obtaining a Head equal to p > 0) is tossed repeatedly and independently until the flrst head is observed. Compute the probability that the flrst head appears at an even
