STAT 251 Lecture Notes - Lecture 7: Sample Space, Ice Cream Cone
STAT 251
Homework Assignment #3
"Due:" Tuesday, October 10, 2017
Reading Assignment
Chapter 5
Problems:
Chapter 5: See below for #1 and #2, Book: 6, 7, 9, 11, 12, 26, 34, 36, 39, 40
1. Pizza Discount. A local pizza restaurant has a spinner with 6 spaces on it. The spaces are the same size
(1/6 of the wheel) and each space is worth a certain discount on a large pizza: $0.00, $0.50, $1.00, $1.50,
$2.00, $3.00. Each customer who comes in to order a large pizza gets to spin the wheel twice. (The
discount they receive on their pizza will be the sum of the two spins of the wheel.)
a. Describe a trial of the random process and give a possible outcome.
b. Given the sample space below, determine the following. (Be sure to verify the sample space to
yourself.)
i. Determine the probability a customer gets a discount of $1.50 on his/her two spins.
ii. Determine the probability that a customer gets some kind of discount on his/her two spins.
iii. Determine the probability a customer gets at least a discount of $2.00.
S =
0,0
0,0.50
0,1.00
0,1.50
0,2.00
0,3.00
0.50,0
0.50,0.50
0.50,1.00
0.50,1.50
0.50,2.00
0.50,3.00
1.00,0
1.00,0.50
1.00,1.00
1.00,1.50
1.00,2.00
1.00,3.00
1.50,0
1.50,0.50
1.50,1.00
1.50,1.50
1.50,2.00
1.50,3.00
2.00,0
2.00,0.50
2.00,1.00
2.00,1.50
2.00,2.00
2.00,3.00
3.00,0
3.00,0.50
3.00,1.00
3.00,1.50
3.00,2.00
3.00,3.00
2. Random Ice Cream Prices. Suppose that an ice cream shop runs a special promotion where they
determine the price of a small ice cream cone by rolling a pair of fair six-sided dice. The price (in cents)
is the larger number followed by the smaller number. (For example, if you roll a 3 and 5, the price would
be 53 cents. If you roll a 3 and 3, the price will be 33 cents.)
a. Describe a trial of the random process and give a possible outcome.
b. Write out the sample space for the random process in (a).
c. How many outcomes are in the sample space?
d. Determine the probability the price will be 23 cents.
e. If you enter the ice cream shop with only one quarter, what is the probability you will be able to
buy an ice cream cone? What if you have two quarters?
f. If I offer to buy your ice cream cone if the price is an odd number, what is the probability that I’ll
buy?
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Document Summary
Chapter 5: see below for #1 and #2, book: 6, 7, 9, 11, 12, 26, 34, 36, 39, 40: pizza discount. A local pizza restaurant has a spinner with 6 spaces on it. The spaces are the same size (1/6 of the wheel) and each space is worth a certain discount on a large pizza: sh. 00, sh. 50, . 00, . 50, Suppose that an ice cream shop runs a special promotion where they determine the price of a small ice cream cone by rolling a pair of fair six-sided dice. The price (in cents) is the larger number followed by the smaller number. (for example, if you roll a 3 and 5, the price would be 53 cents.
