Each problem in this homework is worth 10 points unless otherwise indicated.
- Social security numbers in the US contain 9 digits in the following format:
012 - 345 - 6789
Area # Group # Serial #
Assume that any number (0-9) is possible for each digit.
(5 points each)
- How many different social security numbers are possible?
- What is the probability that a social security number starts with a 5?
- For a given area number, how many different social security numbers are possible?
- Suppose a hacker gets a hold of the last four numbers of your social security number (the serial number). What is the probability that the hacker randomly guesses your full social security number?
- A compact disc (CD) contains 15 songs. How many different playing orders are possible for the 15 songs on the CD?
- John has a standard deck of cards. After shuffling them, he deals you a 5 card hand. What is the probability that your hand contains a royal flush (an ace, king, queen, jack and ten of the same suit)? Note: the order that the cards are dealt is not important here.
- On The Price is Right game show, a Showcase Showdown occurs where three contests are asked to spin the Big Wheel which contains 20 sections showing values from 5¢ - $1.00 in increments of 5¢. If in one round of the Showcase Showdown 3 contestants spin the Big Wheel, what is the probability that all 3 contestants spin an amount over 75¢ on their first spin?
- A computer company produces laptops. For this particular company, for every 100 laptops made one laptop is defective. If Lindsay goes shopping for 20 laptops, what is the probability that 3 of the laptops are defective?
- A company is composed of 5 senior executives, 10 executives and 5 secretaries. A 5 person committee is formed to attack a particular issue.
- How many different 5 person committees are possible?
- If the committee must be composed of 2 senior executives, 2 executives and 1 secretary, how many different 5 person committees are possible?
- A bag contains a red marble, a blue marble and a yellow marble. A marble is selected at random 4 times with replacement. How many events will form a full group of events? Also, list all of these events in which the first draw results in a red marble being selected.
- A cube has all of its sides painted in blue and then is cut into 343 cubes of the same size. All cubes are placed in an urn and are thoroughly mixed, so that the probability of being randomly picked from the urn is the same for all cubes. What is the probability that a randomly picked cube has at least one of its sides painted blue?
- A Rubik’s cube in which each side is painted one of six colors (white, orange, red, blue, green and yellow).
Suppose each side of the Rubik’s cube consists of only one color, if the Rubik’s cube is tossed 6 times what is the probability that the cube will land on the red side at least 4 times?
Complementary problem (worth up to 3 extra credit points)
- There are twelve raffle tickets, three of which are winners. Find the probability that in a sample of 5 tickets there will be no more than one winning ticket.