5) A Professor conducts an exam in a class with 24 boys and 16 girls. 6 boys and 4 girls make an A in thecourse.a)Write the joint pohahility matrix of the gender of the student and his/her grade (A or no A).b)Find the marignal probabilities of a student being a boy or a girl and the marginalprobabilities of a student making or not making an A in the course.Show that the gender of a student and whether he/she makes an A in the course, areindependent.

Answered: 5) A Professor conducts an exam in a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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[part2_Item#1AA] (Probability of an Event and Mutually Exclusive Events) THIS IS NOT A MULTIPLE CHOICE!
You have 5 choices of shirts: Red, blue, green, yellow, brown; 3 choices of pants: Green, brown, black; 4 choices of socks: Black, brown, tan, white; 3 choices of shoes: White, brown, black. What is the probability that you will dress all in brown-shirt, pants, socks, and shoes?
Say that COOP Ale Works, an Oklahoma brewery, uses three production lines to manufacture beer cans. The table below gives percentages of nonconforming cans, categorized by the type of nonconformity, for each of the three lines during a particular year. During this period, line 1 produced 500 nonconforming cans, line 2 produced 400 such cans, and line 3 was responsible for 600 nonconforming cans. Suppose that one of these 1500 cans was selected at random. Table attached in Image. a. What is the probability that the can was produced by line 1? b. What is the probability that the reason for nonconformance is a crack? c. If the selected can came from line 1, what is the probability that it had a blemish? d. Given that the selected can had a surface defect, what is the probability that it came from line 2?
. Three airlines serve a Srinagar. Airline ‘Amira’ has 50% of all the scheduled flights,airline ‘Biyas’ has 30%, and airline ‘chinar’ has the remaining 20%. Their on-time ratesare 80%, 65%, and 40%, respectively. Part 1) Draw the Probability tree diagram. (Note: You may use any software for this, likeMS paint, MS office, etc.) Part 2) A plane has just left on time. What is the probability that it was airline ‘Amira’?
A WAL*MART manager has five good light bulbs and four defected light bulbs in Box 1 and four good light bulbs and five defected light bulbs in Box 2. If the manager transfers one light bulb at random from Box 1 to Box 2, what is the probability of his then drawing a good light bulb from Box 2? (Round to four decimal places. Do not use %)
A PhD graduate has applied for a job with two universities, A and B. The graduate feels that she has a 60% chance of receiving an offer from university A, and a 30% chance of receiving an offer from university B. If she receives an offer from university B, she believes that she has an 70% chance of receiving an offer from university A. What is the probability that both universities will make her an offer? a) 0.66. b) 0.24. c) 0.3
The distribution of car rental by municipal members from the three companies is as follows:60% from company1, 30%from company2 and 10% from company3. According to historical data, 9% of vehicles from company1, 20% of vehiclesfrom company2 and 6% of vehicles from company3 require maintenance,a) What is the probability that a vehicle rented to the municipality will require maintenance?b) What is the probability that the vehicle that needs maintenance is from the 2nd company?
A cybercafe buys 45% of its laptop from Company A, 35% from Company B and 20% from Company C. However, 20% of laptop from Company A is prone to defect whereas 10% from Company Band 5% from Company C. Draw a tree diagram for the situation and hence find the probability the laptop is from Company Cif it is defect.
The client company data from the Decision Dilemma reveal that 155 employees worked one of the 4 types of positions. Shown here are again is the raw values matrix called contingency table with frequency counts for each category and for subtotals and totals containing a breakdown of these employees by type of position and sex. If an employee of the company is selected randomly, what is the probability that the employee is female or a professional worker? Company Human Resource data: SEX Type of position Male FEMALE MANAGERIAL 8 3 11 Professional 31 13 44 Technical 52 17 69 clerical 9 22 31 100 55 155
Pakistan Cricket Board in its central contract places its International players in four different categories, Category A, Category B, Category C and Emerging Players’ Category. Batsmen who are going to play in upcoming series fall into these four categories in the proportions 35 percent, 30 percent, 25 percent and 10 percent. The probability that a Category A player will got out without scoring a run is 0.01, for Category B player its 0.05, for Category C player its 0.02 and the probability that an emerging player will got out on Zero is 0.08. During a match after the fall of second wicket captain sent Muhammad Rizwan on batting and he got out on Zero. What is the probability that Muhammad Rizwan is; In Category A In Category B In Category C

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