15 points My Notes Ask Your Teacher Challenge Problem! This problem will put you

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15 points My Notes Ask Your Teacher Challenge Problem! This problem will put your understanding of the concepts learned in this section to the test. Detailed hints and tips are provided to help you along, but this problem will still take a good amount of time and effort on your part. Be patient and don't be discouraged if you don't get it right away. This problem is designed to challenge you are you up for the challenge? Scenario 1: Kathy drives down Hillsborough Street on Tuesday and Wednesday. Suppose that on any given day there is a 29% chance that she will have to stop for the stoplight at Brooks Ave Hints and Tips Draw a tree diagram for this scenario. CHint: Do this by branching up first to "stops on Tuesday" and "doesn't stop on Tuesday". Then from each of those branch up to 'stops on Wednesday" an d "doesn't stop on Wednesday Figure out which numbers need to be inserted on each of the branches and "multiply up" to find the probabilities for each of the four outcomes Note: In order to be successful with Scenarios 2 and 3 it is important to fully understand how find the Scenario 1 answers using the tree diagram described.) Use this tree to answer the following questions. (Give your answers correct to three decimal places.) (a) What is the probability that she will have to stop at the stoplight on Tuesday? (b) What is the probability that she will have to stop at the stoplight on both Tuesday and Wednesday? (c) What is the probability she has to stop for the stop light on exactly one of the two days? Scenario 2: April drives down Hillsborough Street on Thursday and Friday. Suppose you know that the probability she has to stop for the stoplight at Brooks Ave. on both days is 0.31. What is the probability that April will have to stop on any given day? Hints and Tips Again, you will need to draw a tree diagram. The overall layout of the tree will look similar to your tree for Scenario 1, however, this time you are not given enough information to place any numbers in your tree. To overcome this, we will assign a variable ("p") to be equivalent to P(stops on any given day). Place "p" in your tree in the appropriate places. Since we have set P(stops on any given day) "p his means that doesn't stop on a given day) must be equal to 1 p". Place "1 p in your tree in the appropriate places. Using algebra, "multiply up" your branches to find the probability of each of the four outcomes (if you do this correctly each probability will be a mathematical statement with "p" in it) Now that you have your tree diagram with all the probabilities in terms of "p ook at the information that you were given "Suppose you know that the probability she has to stop for the stoplight at Brooks Ave. on both days is 0.31 Where would this 0.31 go in your tree? Use that information to write an algebraic equation. Solve this equation for "p what is the probability that April will have to stop on an given day? r, equivalently, what is the exact value of "p" in this scenario our answer correct to three decimal places (Give

Explanation / Answer

Scenario 1 :

(a) The probability that she have to stop at stoplight on Tuesday = p( on any given day) = 0.29

(b) The probability that she have to stop at stoplight on Tuesday and Wednesday = p( on two consecutive days) = 0.292 = 0.0841

(c) Probability that she has to stop at stoplight on one out of two day. = p( stop on tuesday ) * p( no stop at wednesday) + p( stop on wednesday) * p( no stop on tuesday) = 0.29 * 0.71 + 0.29 * 0.71 = 0.4118

Q.2 So, here to stop at the light, probability she has to stop at stoplight = 0.31 = p(stop at stoplight at tuesday) * P( stop at stoplight at friday)

so 0.31 = [ p(stop at any given day)] 2

p(stop at any given day) = sqrt(0.31) = 0.5567

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