please answer all the questions and show working as well Take Home Assignment 2

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please answer all the questions and show working as well

Take Home Assignment 2 - Probability Show all workings for all parts of the questions Question 1 Filling orders (6 marks) Andrew, Britney and Chris fill orders in a fast-food restaurant. The table below records the numbers of correct and incorrect orders that they filled on a randomly selected day. Andrew 63 7 70 Chris 47 3 50 Total Correct Incorrect Total Britney 70 10 80 An order has just been filled (a) What is the probability that Andrew filled the order? (b) If it is filled by Chris, what is probability that it is incorrectly filled? (c) What is the probability that it is filled by Britney and is correctly filled? (d) Who filled the order is unknown, but it was incorrectly filled? What is the probability Chris filled the order? (e) Is there a dependency between whether an order is filled correctly and the person who filled it? Explain clearly with the aid of calculated probabilities and appropriate justification Question 2 Public vs Private School (4 marks) The Private School Association conducts a survey of the outcome of private and public school students who pursue university education. The outcome is either graduate eventually or not. It is found that: · 60% of commencing freshmen are from public schools · 75% of public student students who commence their university education eventually graduate · 90% of private school freshmen eventually graduate Is there any evidence that a freshman's chance to graduate is dependent on the type of high school they attended? HINT: you need to construct your own pivot table with a supposed number of students e.g. 1000

Explanation / Answer

Part (a)

Out of 200 orders filled, Andrew filled 70 orders. Hence,

P(Andrew filled the order) = 70/200 = 0.35 ANSWER

Part (b)

Out of 50 orders filled by Chris, 3 orders were incorrect. Hence,

P(order is filled incorrect if Chris filled the order) = 3/50 = 0.06 ANSWER

Part (c)

Out of 200 orders filled, Britney and Chris together filled 130 orders. Hence,

P(Britney or Chris filled the order) = 130/200 = 0.65 ANSWER

Part (d)

Out of 180 correctly filled orders, 47 were filled by Chris. Hence,

P(Chris filled the order given it is filled correct) = 47/180 = 0.26 ANSWER

Part (e)

Out of 200 orders filled, 63 were filled by Andrew and also correctly. Thus, the joint probability of Andrew filling the order and the order being filled correctly, is 63/200.

The marginal probability of Andrew filling the order =70/200 and the marginal probability of the order being filled correctly is 180/200.

Now, (70/200) x (180/200) = 63/200

i.e., joint probability = product of marginal probabilities implying independence of the involved events.

Out of 200 orders filled, 70 were filled by Britney and also correctly. Thus, the joint probability of Britney filling the order and the order being filled correctly, is 70/200.

The marginal probability of Britney filling the order = 80/200 and the marginal probability of the order being filled correctly is 180/200.

Now, (80/200) x (180/200) = 72/200 70/200

i.e., joint probability product of marginal probabilities implying non-independence of the involved events.

Thus, in one case there is independence and the other there is no independence. Hence, it is not correct to say that there is dependency between the correctness of filling and the person filling. ANSWER

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