Question

ap statistics: chapter 5 test form 2

1. according to a report for veterinarians in the united states, 36.5 percent of households in the united states own dogs and 30.4 percent of households in the united states own cats. if one household in the united states is selected at random, what is the probability that the selected household will own a dog or a cat?

a. 0.111
b. 0.331
c. 0.558
d. 0.669
e. not enough information given to determine the probability.

1. the table below shows the responses from 103 people when asked if they support a proposal to expand the public library.

	under the age of 55	age 55 or older	total
no	42	36	78
total	59	44	103

one person from those who responded will be selected at random. which of the following is closest to the probability that the person selected will be someone who responded no, given that the person selected is age 55 or older?
a. 0.350
b. 0.427
c. 0.462
d. 0.757
e. 0.818

Explanation:

Question 1

Step1: Recall Probability Union Formula

The formula for \( P(A \cup B) \) is \( P(A) + P(B) - P(A \cap B) \). Here, \( A \) is owning a dog (\( 36.5\% = 0.365 \)) and \( B \) is owning a cat (\( 30.4\% = 0.304 \)). But we don't know \( P(A \cap B) \) (the probability of owning both a dog and a cat).

Step2: Analyze the Options

Since we lack the intersection probability, we can't calculate \( P(\text{dog or cat}) \) using the given data. So we need to check if there's enough info.

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B)=\frac{P(A \cap B)}{P(B)} \). Here, \( A \) is "responded no" and \( B \) is "age 55 or older". From the table, \( n(A \cap B) = 36 \) (number of people age 55 or older who responded no) and \( n(B) = 44 \) (total number of people age 55 or older).

Step2: Calculate the Probability

Using the formula for probability (since all outcomes are equally likely), \( P(\text{no} | \text{age 55 or older})=\frac{\text{Number of age 55 or older who said no}}{\text{Total number of age 55 or older}}=\frac{36}{44}\approx0.818 \)? Wait, no, wait: Wait, the table: Age 55 or older total is 44, and "no" for age 55 or older is 36? Wait, no, let's check the table again. The table:

• Under 55: Yes=17, No=42, Total=59
• Age 55 or older: Yes=8, No=36, Total=44
• Total: Yes=25, No=78, Total=103

So for conditional probability \( P(\text{No} | \text{Age 55 or older})=\frac{\text{No and Age 55 or older}}{\text{Age 55 or older}}=\frac{36}{44}\approx0.818 \)? But the options have E as 0.818. Wait, but the marked answer in the image is A, but let's recalculate. Wait, maybe I misread. Wait, no: Wait, the question is "the person selected will be someone who responded no, given that the person selected is age 55 or older". So numerator: number of age 55 or older who said no (36), denominator: number of age 55 or older (44). So \( 36\div44\approx0.818 \), which is option E. Wait, but the image has a mark on A, maybe a mistake. But following the table:

Wait, let's recalculate: 36 divided by 44. 36 ÷ 44 ≈ 0.818. So:

Step1: Identify the Counts

From the table, number of people age 55 or older who responded no: 36. Total number of people age 55 or older: 44.

Step2: Apply Conditional Probability

\( P(\text{No} | \text{Age 55 or older})=\frac{36}{44}\approx0.818 \)

Answer:

E. Not enough information given to determine the probability.

Question 2