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Find the expected value. Mr. Cameron is sponsoring an summer concert. He estimates that he will?

  • Question 9 Find the expected value. Mr. Cameron is sponsoring an summer concert. He estimates that he will make $300,000 if it does not rain and make $60,000 if it does rain. The weather bureau predicts the chance of rain is 0.34 for the day of the concert. An insurance company is willing to insure the concert for $150,000 against rain for a premium of $30,000. If he buys this policy, what are his expected earnings from the concert? Answer $270,000 $180,000 $300,000 $239,400 Samantha is taking courses in math and English. The probability of passing math is estimated at 0.4 and English at 0.6. She also estimates that the probability of passing at least one of them is 0.8. What is her probability of passing both courses? Answer 0 0.8 0.2 0.12 Use Bayes' rule to find the indicated probability. An water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock P(R) = 0.53. The clay probability is P(C) = 0.21. The sand probability is P(S) = 0.26. It if it rock, a geological test gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test gives a 75% accuracy for sand. Given the test is positive, what is the probability that soil is rock, P(sand | positive)? Answer P(sand | positive) = 0.26 P(sand | positive) = 0.405 P(sand | positive) = 0.385 P(sand | positive) = 0.209 please explain how to solve them. thanks :)

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    Do your own homework, all these questions are of the same type,

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Mr. Cameron is sponsoring an summer If it rains, he would earn 60,000-30,000+150,000 = 180,000 If it doesn't rain, he would earn 300,000-30,000 = 270,000 Expected earnings = 180,000(0.34)+270,000(0.66) = $239,400 --------------------------------------… Samantha is taking courses in math and English A = pass math B = pass English P(A)=.4 P(B)=.6 P(A U B) = 0.8 P(A U B) = P(A) + P(B) - P(A ∩ B) 0.8 = .4 +.6 - 0.2 P( A ∩ B) = 0.2 --------------------------------------… An water well is to be drilled P(R)=0.53 P(C)=0.21 P(S)=0.26 Let X = positive result P(X/R) = .35 P(X/C) = .48 P(X/S) = .75 P(S/X) = ? P(S/X) = P(S) P(X/S) / [ P(R) P(X/R) + P(C) P(X/C) + P(S) P(X/S) ] --- Bayes' theorem P(S/X) = (0.26)(0.75) / [ (0.53)(0.35) + (0.21) (0.48) +(0.26)(0.75)] = 0.405

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