Final answer:
There are 18 students who passed only Integrated Science, and 27 who passed only Mathematics. The probability that a candidate passed exactly one subject is 75%.
Step-by-step explanation:
To find the number of candidates who passed each subject and the probability that a candidate passed exactly one subject, let's denote Integrated Science passers as 'I' and Mathematics passers as 'M'. Given that 60 students passed either Integrated Science or Mathematics, 15 passed both, and there are 9 more passers in Mathematics than in Integrated Science, we can use the principles of set theory to solve the problem.
First, let's find the number of students who passed each subject. We can express the total number of students who passed at least one subject (60) as the sum of those who passed only one subject or both.
Total passed = Only Integrated Science + Only Mathematics + Both
And we know that:
- Both (passed Integrated Science and Mathematics) = 15
- Only Mathematics = Only Integrated Science + 9
This can be represented as an equation:
60 = I + (I + 9) + 15
From which we can solve for 'I' (the number of students who passed only Integrated Science):
60 = 2I + 24,
36 = 2I,
I = 18.
So, 18 students passed only Integrated Science. To find the number who passed only Mathematics, we add 9:
M = I + 9 = 18 + 9 = 27.
Now, we can calculate the probability that a candidate passed exactly one subject by finding the number of students who passed only one subject (I + M) and dividing by the total number of students (60).
P(Exactly one subject) = (I + M) / Total = (18 + 27) / 60 = 45 / 60 = 0.75 or 75%.