Questions: A total of 80 people were surveyed. The following Venn diagram shows the number of people who like cats and who like dogs. What is the probability that someone likes dogs, assuming that they also like cats (answer choices are in a percentage format, rounded to the nearest whole number)? a.) 51% b.) 41% c.) 71% d.) 21%

A total of 80 people were surveyed. The following Venn diagram shows the number of people who like cats and who like dogs.

What is the probability that someone likes dogs, assuming that they also like cats (answer choices are in a percentage format, rounded to the nearest whole number)?
a.) 51%
b.) 41%
c.) 71%
d.) 21%

Transcript text: A total of 80 people were surveyed. The following Venn diagram shows the number of people who like cats and who like dogs. What is the probability that someone likes dogs, assuming that they also like cats (answer choices are in a percentage format, rounded to the nearest whole number)? a.) $51 \%$ b.) $41 \%$ c.) $71 \%$ d.) $21 \%$

Solution

Solution Steps

Step 1: Identify the total number of people who like cats

From the Venn diagram, the number of people who like cats is the sum of those who like only cats and those who like both cats and dogs. \[ 24 + 17 = 41 \]

Step 2: Identify the number of people who like both cats and dogs

From the Venn diagram, the number of people who like both cats and dogs is given as: \[ 17 \]

Step 3: Calculate the probability that someone likes dogs, given that they also like cats

The probability that someone likes dogs, given that they also like cats, is the ratio of the number of people who like both cats and dogs to the total number of people who like cats. \[ \frac{17}{41} \approx 0.4146 \]