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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Three boxes contain red and green balls. Box 1 has 5 red balls and 5 green balls, Box 2 has 7 red ballsand 3 green balls and Box 3 contains 6 red balls and 4 green balls. The respective probabilities of choosing a box are 1/4, 1/2, 1/4. What is the probability that the ball came from box 2, if it was red?
A class consists of 100 students, 25 of them are girls and 75 boys, 20 of them are rich and the remaining poor, 40 of them are fair complexioned. What is the probability of selecting a fair complexioned rich girl?
According to a theory in genetics, if tall and colorful plants are crossed with short and colorless plants, four types of plants will result: tall and colorful, tall and colorless, short and colorful, and short and colorless, with corresponding probabilities of 5/16, 4/16, 1/16,and 6/16. In a multinomial experiment, if 10 plants are selected, find the probability that 6 will be tall and colorful, 2 will be tall and colorless, 1 will be short and colorful, and 1will be short and colorless. the probability is _____
Q4/ Suppose there are two machines (A, B) in a factory, both producing chairs. Machine A produce twenty percent of their chairs and Machine B produce eighty percent of their chairs. fifteen percent of the chairs come from Machine A are defective and ten percent of the chairs come from Machine B are defective. If a chair is chosen randomly and found to be defective, what is the probability that it came from machine B?
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?
According to a theory in genetics, if tall and colorful plants are crossed with short and colorless plants, four types of plants will result: tall and colorful, tall and colorless, short and colorful, and short and colorless, with corresponding probabilities of 5/16, 4/16, 1/16, and 6/16. In a multinomial experiment, if 10 plants are selected, find the probability that 3 will be tall and colorful, 2 will be tall and colorless, 1 will be short and colorful, and 4 will be short and colorless.
5. A candy dish contains 2 red (R) and 4 yellow (Y) candies. You close your eyes, select two candies from the dish (without replacement), and record their colors. Use general multiplication rule and special addition rule to find the following probabilities. a. The probability that the first selected candy will be red and the second selected candy will be yellow is b. The probability that two selected candies will be of different colors_ One is red, another one is yellow c. Probability that two selected candies will be of the same color_ Both are red or both are yellow Assuming that the event "The first selected candy will be red and the second selected candy will be yellow "is denoted by A, the event "Two selected candies will be of different colors" is denoted by B, and the event "Two selected candies will be of the same color" is denoted by C, show your work in finding P(A), P(B), and P(C) in the questions a, b, and c.
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.
A poll conducted on the proposed bonus plan for employees indicated that 40% of all female employees and 65% of all night-shift employees supported the plan. Also, 34% of all employees are women, 51% of all employees are night-shift workers, and 24% are day-shift females. If two employees are randomly selected, what is the probability that the first, a male is a night-shift worker and the second, a female is a day-shift worker? Answer:
A social event allows free entrance to those with Aim High credit card or those with the car Elite. The probabilities of having Aim High and Elite among the employees of a company are 0.10 and 0.05, respectively. Having Aim High is found to be independent of owning Elite. If 1,000 invitations are sent randomly to employees of the company, estimate the number who will be given free entrance.

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