A survey was conducted between males and females to see if they prefer cheeseburgers or hamburgers. The results of the survey are posted in the Venn diagram below.
Cheeseburger: 26
Female: 18
Both: 21
Neither: 16
Find the probabilities as percents...
Cheeseburger|Female
Hamburger|Male
Cheeseburger
To find the probabilities as percents, we need to divide the number in each category by the total number of participants and then multiply by 100.
Let's calculate each probability step by step:
1. Cheeseburger|Female:
The number of people who prefer cheeseburgers and are female is 18. The total number of participants is 26.
Probability = (18/26) x 100 = 69.23%
Therefore, the probability of choosing a cheeseburger given that the person is female is 69.23%.
2. Hamburger|Male:
To calculate this probability, we need to know the total number of males who participated in the survey. Unfortunately, that information is not given in the question, so we cannot calculate this probability.
3. Cheeseburger:
The number of people who prefer cheeseburgers is 26. The total number of participants is 26.
Probability = (26/26) x 100 = 100%
Therefore, the probability of choosing a cheeseburger overall is 100%.
To find the probabilities as percents, we need to determine the total number of respondents.
The information provided in the problem gives us the following values:
Cheeseburger: 26
Female: 18
Both: 21
Neither: 16
To find the total number of respondents, we need to add the number of people who prefer cheeseburgers and the number who prefer hamburgers but not both. We can calculate this as:
Total respondents = Cheeseburger + Hamburger (but not both)
Total respondents = 26 + (18-21) = 26 - 3 = 23
Now, we can find the probabilities as percents:
1. Probability of choosing a cheeseburger, given that the person is female:
To find this probability, we need to divide the number of females who prefer cheeseburgers by the total number of females:
Cheeseburger | Female = (Number of females who prefer cheeseburgers / Total number of females) x 100
Cheeseburger | Female = (18 / 23) x 100
Cheeseburger | Female ≈ 78.26%
2. Probability of choosing a hamburger, given that the person is male:
To find this probability, we need to subtract the number of people who chose a cheeseburger from the total number of respondents (since they cannot choose both), and then divide it by the total number of males:
Hamburger | Male = ((Total number of males - Both) / Total number of males) x 100
Hamburger | Male = ((23 - 21) / (23-18)) x 100
Hamburger | Male = (2 / 5) x 100
Hamburger | Male = 40%
3. Probability of choosing a cheeseburger:
To find this probability, we need to divide the number of people who prefer cheeseburgers (regardless of gender) by the total number of respondents:
Cheeseburger = (Number of people who prefer cheeseburgers / Total number of respondents) x 100
Cheeseburger = (26 / 23) x 100
Cheeseburger ≈ 113.04%
Note: The percentages are approximated to two decimal places for clarity.