Question

California University encourages professors to consider using e-textbooks instead of the traditional paper textbooks. Many courses have adopted the new e-textbook option. Suppose that the random variable X represents the number of courses taken by a student during the Winter 20 semester at California University that provide an e-textbook option. The (partial) probability distribution for the random variable X is provided.

X = # course with e-text option	0	1	2	3	4	5
Probability	_____	_____	0.30	0.25	0.15	0.10

Suppose the probability that only 1 course provides an e-textbook option is three times as likely as the probability of 0 courses providing an e-textbook option.
Melissa is not your typical Califonia University student, she is often looking for environmentally friendly options. She heard about the University's initiative and, when registering for courses, she decided to purposely look for classes that offered the e-textbook option. Knowing that the number of courses she takes that offer an e-textbook option this semester is above the mean, what is the probability that all 5 of her classes have an e-textbook option?   

Assume we randomly select 7 students at California University who are enrolled in courses this Winter semester. What is the probability that exactly 3 students reported taking 2 or more courses that offer an e-textbook option this Winter semester?
Show your work: write down the formula, then plug in values, then provide the answer.

Answer 1

P( 2 or more ) = 0.30+0.25+0.15+0.10 = 0.80

n = 7 , x = 3

P( 7 , 3 ) = ⁷ C ₃ (P)^x (1-P)^n-x

  = 35 (0.80)³ (0.20)⁴

  = 0.0287