Of all the grade 12 students in a school, 27% take Science Fiction, 34% take Data Management and 9% take both courses. Given that a student is taking Science Fiction, what is the probability that they are also taking Data Management? Also, is this a mutually exclusive event? Feel free to do this by hand and upload your image.
Disregard the actual number of students. Consider a group of 100 students divided up the same way
9 of the 27 SF students take DM. So, the probability is 33%
what do you mean by divided up the same way?
I'm sorry but do you mind explaining how you got 33%
27% means 27 out of 100
assuming 100 total makes it easy.
9 out of the 27 take both
(9/27) * 100 = 33.33333333 %
which is about 33%
To find the probability that a student taking Science Fiction is also taking Data Management, we need to use conditional probability.
First, let's define the events:
A = student taking Science Fiction
B = student taking Data Management
We are given the following information:
P(A) = 27% = 0.27
P(B) = 34% = 0.34
P(A ∩ B) = 9% = 0.09 (both courses)
The conditional probability formula is:
P(B|A) = P(A ∩ B) / P(A)
Substituting the values, we have:
P(B|A) = 0.09 / 0.27
Calculating this expression, we find:
P(B|A) ≈ 0.333
So, the probability that a student taking Science Fiction is also taking Data Management is approximately 0.333 or 33.3%.
Now let's address whether these events are mutually exclusive.
Two events are mutually exclusive if the occurrence of one event means that the other event cannot occur at the same time. In this case, if taking Science Fiction and taking Data Management were mutually exclusive, then the probability of taking both courses (P(A ∩ B)) would be 0.
Since P(A ∩ B) = 0.09 > 0, we can conclude that these events are not mutually exclusive. There are students who take both Science Fiction and Data Management.