Business Mathematics IHomework 4Solution.Solution.Business Mathematics IHomework 4Prepared forStephen ReyesMath 115a, Section University of Arizona ByName of studentSubmitted onDateI affirm that I completed this assignment in its entirety and that the work contained herein is original. Furthermore, I understand that sanctions will be imposed if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for this course. ______________________________ ______________________________Name (typed) Signature1. (Conditional Probability) Consider the experiment of rolling a fair die twice. All of the 36 outcomes in the sample space, S, are equally likely. Let F be the event that the product of thefaces is greater than 18 and G be the event that the product of the faces is even. Compute)|( GFP and )|( FGP.Solution. 2. (Conditional Probability) Consider the experiment of tossing a fair coin twice. Each of the four outcomes in the sample space, S, is equally likely.)}( ),( ),( ),{( TTTHHTHHS Let E be the event that the first toss is heads, F be the event that both tosses are heads, and G be the event that at least one toss is heads. Are E and G independent?Solution. 3. (Conditional Probability) Consider newly incorporated business in a certain area. Data indicates that there is a 69% chance that a business fails within the first year, a 21% chance that a business is its owner’s first venture, and a 19% chance that a business fails during the first year and that it is its owner’s first venture. Let F be the event that a business fails within the first year and V be the event that a business is its owner’s first venture. Compute)|( VFP and )|( FVP.Solution. 4. (Conditional Probability) Suppose that a telemarketer uses random-digit dialing equipment to call three residential telephone numbers at random. There is a 20% chance of reaching a live person with each call, and the calls are independent. (i) What is the probability that the telemarketer reaches a live person with the first two calls but not the third? (ii) What is the probability that exactly two of the calls reach a live person? (Hint: This can happen in three mutually exclusive ways.)Solution.
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