A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.
Outcomes Probability
OEE EEO OOE OEO OOO EOO EEE EOE
Event A: An even number on the last roll
Event B: Two or more even numbers
Event C: No even numbers on the last two rolls
Outcomes Probability
OEE 1/8
EEO 1/8
OOE 1/8
OEO 1/8
OOO 1/8
EOO 1/8
EEE 1/8
EOE 1/8
Event A: An even number on the last roll
The outcomes contained in Event A are: OEE, OOE, OEO, and EOE.
The probability of Event A is 4/8 = 1/2.
Event B: Two or more even numbers
The outcomes contained in Event B are: OEE, EEO, OOE, and EOE.
The probability of Event B is 4/8 = 1/2.
Event C: No even numbers on the last two rolls
The outcomes contained in Event C are: OOO, EOO, and EEE.
The probability of Event C is 3/8.
Town officials want to estimate the number of households that own a dog. Answer the following.
(a) Which of the following surveys probably would best represent the entire population of households?
50 households with a garage are randomly selected; 19 own a dog.
50 households within a mile of a park are randomly selected; 25 own a dog.
50 households are randomly selected from the town; 14 own a dog.
(b) There are 550 households in the town.
Using your answer from part (a), estimate the number of households that own a dog.
households
(a) The survey that would probably best represent the entire population of households is the survey where 50 households are randomly selected from the town and 14 own a dog.
(b) To estimate the number of households that own a dog, we can set up a proportion using the survey results from part (a).
Let x be the number of households that own a dog.
14/50 = x/550
Cross-multiplying, we get:
14 * 550 = 50x
7700 = 50x
Dividing both sides by 50, we have:
x = 154
Therefore, we estimate that there are 154 households in the town that own a dog.
A political campaign wants to estimate the number of adult residents who voted in the last city election. Answer the following.
(a) Which of the following surveys probably would best represent the entire adult population of the city?
25 adult residents are randomly selected from the city; 11 voted in the last election.
25 senior residents are randomly selected; 13 voted in the last election.
25 homeowners are randomly selected; 16 voted in the last election.
(b) There are 21,400 adults who live in the city. Using your answer from part (a), estimate the number of adults who voted in the last city election.
adults
(a) The survey that would probably best represent the entire adult population of the city is the survey where 25 adult residents are randomly selected from the city and 11 voted in the last election.
(b) To estimate the number of adults who voted in the last city election, we can set up a proportion using the survey results from part (a).
Let x be the number of adults who voted in the last city election.
11/25 = x/21400
Cross-multiplying, we get:
11 * 21400 = 25x
235400 = 25x
Dividing both sides by 25, we have:
x = 9416
Therefore, we estimate that 9416 adults voted in the last city election.