60 Math 116 – 02: HW Project #7
Name:
Due Friday, October 24, 2014
1. A survey of local car dealers revealed that 64% of all cars sold last month had CD players,
28% had alarm systems, and 22% had both CD players and alarm systems. (4 points each)
(a) What is the probability one of these cars selected at random had neither a CD player
nor an alarm system?
(b) What is the probability that a car had a CD player unprotected by an alarm system?
(c) What is the probability a car with an alarm system had a CD player?
2. For purposes of making budget plans for staffing, a college reviewed student’s year in school
and area of study. Of the students, 22.5% are seniors, 25% are juniors, 25% are sophomores,
and the rest are freshmen. Also, 40% of the seniors major in the area of humanities, as did
39% of the juniors, 40 % of the sophomores, and 36% of the freshmen. (4 points each)
(a) What is the probability that one of these students, selected at random, majors in the
humanities?
(b) What is the probability that a randomly selected humanities major is a junior?
(c) What is the probability that a randomly selected non-humanities major is a senior?
3. A survey of an introductory statistics class in Autumn 2003 asked students whether or not
they ate breakfast the morning of the survey. Results are as follows. (4 points each)
Yes
No
Total
Male
66
66
132
Female
125
74
199
Total
191
140
331
(a) What is the probability that a randomly selected
student is female?
(b) What is the probability that a randomly selected
student ate breakfast?
(c) What is the probability that a randomly selected
student is a female who ate breakfast?
(d) What is the probability that a randomly selected
student is female, given that the student ate
breakfast?
4. A biology professor responds to some student questions by e-mail. The probability model
below describes x = the number of e-mails that the professor may receive from students
during a day. Suppose he never gets more than 5 e-mails from students in a day.
x
0
1
2
P(x)
0.05
0.15
0.22
3
4
5
0.28
0.07
(a) What is the probability that the professor gets 3 e-mails from students?
(2 points)
(b) Find the average number of e-mails ( m ( x )) and the standard deviation in the number
of e-mails (s ( x )) that the professor gets from students each day. Show all of your
work and calculations – that is, do not just use “1 – Var Stats” in the calculator.
(8 points)
5. You play two games against the same opponent. The probability that you win the first game
is 0.42. If you win the first game, the probability you also win the second game is 0.24. If
you lose the first game, the probability that you win the second is 0.35. Let X be the number
of games you win against this opponent. Construct the probability distribution of X. (10 points)