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Exam 5: Probability

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Question 31

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A small manufacturing firm has 250 employees. Fifty have been employed for less than 5 years and 125 have been with the company for over 10 years. Suppose that one employee is selected at random from a list of the employees. For the following events, compute the probabilities requested below. A = the event the selected employee has been with the firm less than 5 years B = the event the selected employee has been with the firm 5 ≤ x ≤ 10 years. C = the event the selected employee has been with the firm over 10 years. ​ a)P(A)b)P(C)c)P(A or B)d)P(A and C)

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Question 32

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At Thomas Jefferson High School students are heavily involved in extra-curricular activities. Suppose that a student is selected at random from the students at this school. Let the events A, M, and S be defined as follows, with probabilities listed: ​ Calculate each of the following (show your work): i) ii) iii)

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i).5625
ii...

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Question 33

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Students in two classes of upper-level mathematics were classified according to class standing and gender, resulting in the following table. Define events A, B, and C as follows: A = the event that the selected student is a female B = the event that the selected student is a male C = the event that the selected student is a senior. In the following table indicate by putting an X in the appropriate cells which is true for each pair of events. X = Yes, Blank = No

Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% are shipped to people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other people, but for only 10% of orders shipped to the person making the order. a)What is the probability that a randomly selected order will be gift wrapped and sent to another person? b)What is the probability that a randomly selected order will be gift wrapped? c)Is gift wrapping independent of the destination of the gift? Justify your response statistically.

Each of 400 people who purchased a Honda Civic was classified according to gender and whether the car purchased had a hybrid engine or not. Find P (hybrid | male) .

In order to ensure the safety of school classrooms the local Fire Marshall does an inspection at Thomas Jefferson High School every month, looking for faulty wiring, overloaded circuits, etc. At TJHS the new Academic Wing has 5 math rooms, 10 science rooms, and 10 English rooms. The science rooms are divided into 8 biology and 2 chemistry rooms. Each month, the Fire Marshall randomly picks one of the rooms in the new wing to inspect each month. Define the following events: S = the event the selected room is a science room B = the event the selected room is a biology room M = the event the selected room is a math room E = the event the selected room is an English room C = the event the selected room is a chemistry room Calculate the probabilities of the events described below: a)P(S)b)P(M or E )c)P(E or B)d)P(S and not C)

A man has five ties and each day chooses a tie at random to wear to work. He is colorblind and is wife frequently complains that he wears the same tie two days in a row. Your task is to design and conduct a simulation that could be used to estimate the probability that he wears the same tie two days in a row in a 5-day week. a)To simulate the first strategy discussed above, assign digits to the ties that will result in the probability of selection of each tie to be the same. Tie 1 Digits: Tie 2 Digits: Tie 3 Digits: Tie 4 Digits: Tie 5 Digits: ​ b)Describe how you would use a random digit table to conduct one run of your simulation. ​

Experimental studies utilize blinding to prevent researchers from biasing their measurements of the patients. But can they guess the treatment? In a study of a drug intervention, clinicians who were "blinded" were asked to guess what treatment their patients received. Data from that experiment are shown below. Assume that these data are indicative of the population of these treatments. ​ a)If a subject is selected at random, what is the probability that the researcher correctly guesses the treatment? b)If a randomly chosen subject received the standard treatment, what is the probability that the researcher correctly guesses the treatment?

An airline reports that for a particular flight operating daily between Phoenix and Atlanta, the probability of an on-time arrival is 0.64. Give a relative frequency interpretation of this probability. ​

If two events, A and B, are mutually exclusive, then .

As every Girl Scout knows, statistics teachers seriously love Girl Scout Cookies. The number of boxes of GS cookies statistics teachers order, like all important decisions made by statistics teachers, is determined by independent rolls of a 4-sided fair die. If a one appears, 6 boxes are ordered; if any other number appears, 2 boxes are ordered. a)What is the probability that a statistics teacher places an order for 2 boxes of Girl Scout cookies? b)What is the probability that with two independently chosen statistics teachers will each order 6 boxes each? c)What is the probability that for two independently chosen statistics teachers the first will order 6 boxes and the second will order 2 boxes? d)What is the probability that for two independently chosen statistics teachers exactly one will order 6 boxes?

The General Multiplication Rule states that .

Some limitations of the classical approach to probability were discussed in the text. Identify and briefly discuss one of these.

Two events are independent if they cannot occur simultaneously.

Two events, E and F, are independent if .