A survey of 80 employees was conducted asking about which meals they regularly eat at the office. Twenty employees eat breakfast at the office, 50 eat lunch, and 15 eat both breakfast and lunch. If an employee is randomly selected from this group, what is the probability of randomly selecting an employee who eat breakfast or lunch at the office? Explain how you got the answer.
To find the probability of randomly selecting an employee who eats breakfast or lunch at the office, we need to add the probability of selecting an employee who eats breakfast to the probability of selecting an employee who eats lunch, but we need to subtract the probability of selecting an employee who eats both breakfast and lunch to avoid double counting.
P(eats breakfast or lunch) = P(eats breakfast) + P(eats lunch) - P(eats both)
P(eats breakfast) = 20/80 = 0.25
P(eats lunch) = 50/80 = 0.625
P(eats both) = 15/80 = 0.1875
P(eats breakfast or lunch) = 0.25 + 0.625 - 0.1875 = 0.6875
Therefore, the probability of randomly selecting an employee who eats breakfast or lunch at the office is 0.6875 or 68.75%.
To find the probability of randomly selecting an employee who eats breakfast or lunch at the office, we need to calculate the proportion of employees who eat breakfast or lunch out of the total number of employees surveyed.
Let's break down the information given:
- 20 employees eat breakfast at the office
- 50 employees eat lunch at the office
- 15 employees eat both breakfast and lunch
To calculate the total number of employees who eat breakfast or lunch, we need to avoid double counting the 15 employees who eat both. We can do this by adding the number of employees who eat breakfast and the number of employees who eat lunch, and then subtracting the number of employees who eat both.
Total number of employees who eat breakfast or lunch = Number eating breakfast + Number eating lunch - Number eating both
= 20 employees + 50 employees - 15 employees
= 55 employees
Therefore, out of the 80 employees surveyed, 55 eat breakfast or lunch at the office.
Finding the probability is done by dividing the number of favorable outcomes (in this case, employees who eat breakfast or lunch) by the total number of possible outcomes (in this case, the total number of employees).
Probability of randomly selecting an employee who eats breakfast or lunch = Number of employees who eat breakfast or lunch / Total number of employees surveyed
= 55 employees / 80 employees
To simplify this fraction, we can divide both the numerator and denominator by 5:
= 11 employees / 16 employees
Therefore, the probability of randomly selecting an employee who eats breakfast or lunch at the office is 11/16.