Me again. I just have one more question. I want to make sure I understand this question.
60 students were asked about movies they had seen during the past month. 20 of the students had seen a comedy, 15 had seen a horror movie, and 5 had seen both a comedy and a horror movie.
a) Find the probability that a randomly selected student had seen
a horror movie or a comedy (or both).
I drew my venn diagram.
I had 5 in the intersection part since 5 both saw a comedy and a horror movie. For the comedy section, I did 20-5 for 15 in the outermost circle. Then for the horror section, I did 15-5 for 10.
For the probability, would I just set it up like 15/60 (I chose 60 because that is the total) for the comedy and 10/60 for the horror?
number( CUH) = number(C) + numbr(H) - number (C∩H)
= 20 + 15 - 5
= 30
You had 20+ 15 -15-5 =30 , probably a typo in the -15
It asked for the prob P(CUH)
= 30/60 = 1/2
To find the probability that a randomly selected student had seen a horror movie or a comedy (or both), you need to consider the total number of students who have seen a horror movie, the total number of students who have seen a comedy, and the total number of students in the survey.
In this case, you correctly determined that 5 students had seen both a comedy and a horror movie, 15 students had seen only a comedy, and 10 students had seen only a horror movie.
To calculate the probability, you need to add the number of students who have seen a comedy to the number of students who have seen a horror movie, and then subtract the number of students who have seen both because they would be counted twice otherwise.
The total number of students who have seen a comedy or a horror movie (or both) is calculated as:
(15 + 10) - 5 = 20
Therefore, the probability that a randomly selected student had seen a horror movie or a comedy (or both) is:
20/60 = 1/3
So, the correct probability is 1/3, not 15/60 for the comedy and 10/60 for the horror.
Remember to always consider the total number of events in the sample space when calculating probabilities to ensure accurate results.