1) In a U of A class of 30 students, 11 read Arizona Daily Wildcat, 9 read Arizona Daily Star, and 13 read at least one of these newspapers. A randomly selected student is asked whether he or she reads Arizona Daily Wildcat or Arizona Daily Star. Determine the probability that the selected student
(A) Reads both Arizona Daily Wildcat and Arizona Daily Star.
(B) Reads only Arizona Daily Wildcat.
2) A box contains 15 green marble and 17 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without replacement, another white marble?
3) A six sided dime is rolled 3-times. How many different outcomes are possible?
4) Out of 350 applicants for a job, 165 are male and 58 are male and have a graduate degree. What is the probability that a randomly chosen applicant has a graduate degree, given that they are male?
5) Toss a fair coin 3 times.
(A) What is the sample space S.
(B) What is the probability of obtaining exactly 2 heads?
(C) What is the probability of obtaining at least 2 heads?
6) Two cards are to be dealt successively at random and without replacement from a deck of card. What is the probability of receiving in order a diamond and a spade?
7) A quality control inspector has drawn a sample of 15 light bulbs from a recent production lot. Suppose that 10% of the bulbs in the lot are defective.
(A) What is the probability that exactly 5 of the bulbs are defective? Round your answer to 4 decimal places.
(B) What is the probability that at most 2 of the bulbs are defective? Round your answer to 4 decimal places.
(C) What is the probability that at least 1 of the bulbs is defective? Round your answer to 4 decimal places.
(D) What is the expected number of defective bulbs in the sample?
(E) What is the variance of the number of defective bulbs in the sample?
8) Of the people who enter a blood bank to donate blood, 30% has type O+. For the next three people entering the blood bank, let X denote the number with O+ blood. Assume the independence among the people with respect to blood type.
Find the probability that exactly 2 of the people entering the blood bank has type O+ blood.
9) The number of phone calls passing through a particular relay system follows a Poisson distribution with a mean of 3 per minute.
(A) Find the probability that exactly two calls will pass through the relay system during a 1-minute period.
(B) Find the probability that no calls will pass through the relay system during a 2-minute period.
(C) Find the probability that at least two calls will pass through the relay system during a 2-minute period.
(D) Determine the mean and variance of the number of phone call passing through the relay system during a 1-minute period.
10) A company is calculating the cost of equipment maintenance for its budget. In order to decide the budget, the number of machine malfunctions, X, per month is considered. Based on past performance, the distribution of X is given as follows:
|
x
|
p(x)
|
|
0
|
0.1
|
|
1
|
0.3
|
|
2
|
0.5
|
|
3
|
0.1
|
(A) Determine the expected value, variance and standard deviation of the number of mal- functions per month.
(B) Find P (1 ≤ X ≤ 3)
11) In a political science class there are 7 men and 6 women. 3 students are randomly selected to present a topic. What is the probability that at least 1 of the 3 students selected is male?
12) How many ways can we permute the letters in the word INDIANA?
13) (A) Write out the sample space, S, for the given experiment: A die shows 3 different colors on it; red (R), blue (B), and green (G). Give the sample space for the next two rolls.
(B) What is the probability of obtaining RB or BR?
14) The diameters of a ball bearings are normally distributed. The mean diameter is 141 millimeters and the variance is 10.
(A) Find the z-score (standard score) of 143.
(B) Find the probability that the diameter of a selected bearing is less than 143 millimeters.
15) (A) Find the area under the normal curve between z = -0.23 and z = 1.45 Round your answer to four decimal places.
(B) Find the value of z such that 0.40 of the area lies to the left of z. Round your answer to two decimal places.
16) Consider the probability that at most 17 out of 150 DVDs will malfunction. Assume the probability that a given DVD will malfunction is 9%.
(A) Approximate the probability using the normal distribution. Round your answer to four decimal places.
(B) Why can the normal distribution be used to approximate the probability in this problem?
17) Consider the probability that more than 18 out of 150 DVDs will malfunction. Assume the probability that a given DVD will malfunction is 9%.
Approximate the probability using the normal distribution. Round your answer to four decimal places.
18) Consider the probability that exactly 90 out of 152 computers will not crash in a day. Assume the probability that a given computer will not crash in a day is 59%. Approximate the probability using the normal distribution.
19) The following table displays the results of a study, by educational level, of those who have smoked a cigarette within the past year for persons aged 26 and older.
|
Education
|
Smoked
|
Have not smoked
|
Total
|
|
< High School Diploma
|
10,393
|
19,472
|
29,865
|
|
High School Graduate
|
17,798
|
39,247
|
57,045
|
|
Some College
|
13,463
|
30,969
|
44,432
|
|
College Graduate
|
8,320
|
43,357
|
51,677
|
|
Total
|
49,974
|
133,045
|
183,019
|
Table 1. Source: Introduction to Probability and its Applications by R. Scheaffer.
(A) Find the percentage of people who has smoked a cigarette within the past year.
(B) Find the percentage of College Graduates who has smoked a cigarette within the past year.
(C) Find the percentage of people who completed College.
(D) Find the percentage of people who completed College and smoked a cigarette in the past year.
(E) What is the conditional probability that a randomly selected person has completed col- lege given that he/she has smoked a cigarette in the past year?
(F) Are the events"completed college" and"smoked a cigarette within the past year" independent?
20) 6 applicants have applied for three different jobs. How many ways can the jobs be filled.
21) A box contains 15 balls; 3 red, 5 blue and 7 green balls. 8 balls are selected from the box without replacement. What is the probability that the balls selected are 1 red, 4 blue and 3 green?