Description
HW6
A box contains 54 red marbles, 9 white marbles, and 75 blue marbles. If a marble is randomly selected from the box,
what is the probability that it is red or blue? Express your answer as a fraction or a decimal number rounded to four
decimal places.
1.
You are going to play mini golf. A ball machine that contains 19 green golf balls, 20 red golf balls, 24 blue golf balls, and
17 yellow golf balls, randomly gives you your ball. What is the probability that you end up with a red golf ball? Express
your answer as a simplified fraction or a decimal rounded to four decimal places.
2.
A pizza delivery company classifies its customers by gender and location of residence. The research department has
gathered data from a random sample of 1399 customers. The data is summarized in the table below.
Gender and Residence of Customers
Males Females
Apartment 81 228
Dorm 116 79
With Parent(s) 215 252
Sorority/Fraternity House 130 97
Other 129 72
3.
What is the probability that a customer is not male or does not live with parents? Write your answer as a fraction or a
decimal number rounded to four decimal places.
Determine if the following events are independent.
Going to the gym. Losing weight.
4.
Answer: A) Dependent B) Independent
A veggie wrap at City Subs is composed of 3 different vegetables and 3 different condiments wrapped up in a tortilla. If
there are 8 vegetables, 7 condiments, and 3 types of tortilla available, how many different veggie wraps can be made?
5.
Determine if the following events are independent.
Jeff runs out of gas on the way to work. Liz watches the evening news.
6.
Answer: A) Dependent B) Independent
The newly elected president needs to decide the remaining 8 spots available in the cabinet he/she is appointing. If there
are 14 eligible candidates for these positions (where rank matters), how many different ways can the members of the
cabinet be appointed?
7.
A bag contains 9 red, 4 orange, and 9 green jellybeans. What is the probability of reaching into the bag and randomly
withdrawing 4 jellybeans such that the number of red ones is 0, the number of orange ones is 1, and the number of green
ones is 3? Write your answer as a fraction or a decimal number rounded to four decimal places.
8.
1
Evaluate the following expression.
11!
7!
9.
Describe the complement of the given event.
67% of subscribers to a fitness magazine are over the age of 34.
10.
11. If you throw exactly three heads in four tosses of a coin you win $97. If not, you pay me $30.
Step 1. Find the expected value of the proposition. Round your answer to two decimal places.
Step 2. If you played this game 559 times how much would you expect to win or lose? (Losses must be entered as
negative.)
12. Flip a coin 9 times. If you get 4 tails or less, I will pay you $23. Otherwise you pay me $26.
Step 1. Find the expected value of the proposition. Round your answer to two decimal places.
Step 2. If you played this game 994 times how much would you expect to win or lose? (Losses must be entered as
negative.)
2
13. The sensitivity and specificity of the polygraph has been a subject of study and debate for years. A 2001 study of the
use of polygraph for screening purposes suggested that the probability of detecting a liar was .59 (sensitivity) and that
the probability of detecting a “truth teller” was .90 (specificity). We estimate that about 20% of individuals selected for
the screening polygraph will lie.
a. What is the probability that an individual is actually a liar given that the polygraph detected him/her as such? (Show
me the table or the formulaic solution or both.)
b. What is the probability that an individual is actually a truth-teller given that the polygraph detected him/her as
such? (Show me the table or the formulaic solution or both.)
c. What is the probability that a randomly selected individual is either a liar or was identified as a liar by the
polygraph? Be sure to write the probability statement.
