Of the 300 employees that were surveyed, 200 had college degrees, 50 were single, and 30 were both single and had college degrees. What is the probability that an employee chosen at random is single or has a college degree?
Single only = 30/300 = 1/10 = .1
Degree only = 200/300 = 2/3 = .67
Either-or probability is found by adding the probability of the individual events.
To find the probability that an employee chosen at random is single or has a college degree, we need to use the principle of inclusion-exclusion.
Let's label the event "S" as being single and the event "CD" as having a college degree. We are interested in finding the probability of the union of these two events, P(S∪CD), which means either being single or having a college degree.
We are given the following information:
- The total number of employees surveyed is 300.
- The number of employees with college degrees is 200.
- The number of employees who are single is 50.
- The number of employees who are both single and have college degrees is 30.
To calculate the probability, we can use the following formula:
P(S∪CD) = P(S) + P(CD) - P(S∩CD)
First, we need to determine P(S), the probability of being single. Given that 50 out of 300 employees are single, we have:
P(S) = 50/300
Next, we need to determine P(CD), the probability of having a college degree. Given that 200 out of 300 employees have college degrees, we have:
P(CD) = 200/300
Finally, we need to determine P(S∩CD), the probability of being both single and having a college degree. Given that 30 out of 300 employees fall into this category, we have:
P(S∩CD) = 30/300
Now we can substitute these values into the formula to find the probability of an employee being single or having a college degree:
P(S∪CD) = P(S) + P(CD) - P(S∩CD)
P(S∪CD) = (50/300) + (200/300) - (30/300)
P(S∪CD) = (250/300) - (30/300)
P(S∪CD) = 220/300
P(S∪CD) = 22/30
Therefore, the probability that an employee chosen at random is single or has a college degree is 22/30.