In an examination, 60 candidates passed integrated science or mathematics. If 15 passed in both subject and 9 passed in mathematics than integrated
science find the:
1.The number of candidate who passed in each subject.
2.The probability that a candidate passed in exactly one subject.
To find the number of candidates who passed in each subject, we need to use the principle of inclusion-exclusion.
Let's denote:
A: The event that a candidate passed in integrated science.
B: The event that a candidate passed in mathematics.
We are given:
n(AUB) = 60 (the number of candidates who passed in either integrated science or mathematics)
n(B) = 9 (the number of candidates who passed in mathematics)
1. Number of candidates who passed in each subject:
We are given that 15 candidates passed in both subjects (n(A ∩ B) = 15). We want to find n(A) and n(B).
Using the principle of inclusion-exclusion:
n(AUB) = n(A) + n(B) - n(A ∩ B)
60 = n(A) + 9 - 15
n(A) = 66 - 15
n(A) = 51
So, there are 51 candidates who passed in integrated science.
To find n(B), we can use the same equation:
60 = 51 + n(B) - 15
n(B) = 60 - 51 + 15
n(B) = 24
So, there are 24 candidates who passed in mathematics.
Therefore, the number of candidates who passed in each subject is:
Integrated Science: 51
Mathematics: 24
2. To find the probability that a candidate passed in exactly one subject (either integrated science OR mathematics), we need to find the number of candidates who passed in exactly one subject and divide it by the total number of candidates (60).
The number of candidates who passed in exactly one subject can be found by subtracting the number of candidates who passed in both subjects from the total number of candidates who passed in either subject.
n(A U B) - n(A ∩ B) = 60 - 15 = 45
So, the number of candidates who passed in exactly one subject is 45.
Now, we can calculate the probability:
Probability (Passed in exactly one subject) = Number of candidates who passed in exactly one subject / Total number of candidates
Probability (Passed in exactly one subject) = 45 / 60
Probability (Passed in exactly one subject) = 0.75 or 75%
Therefore, the probability that a candidate passed in exactly one subject is 0.75 or 75%.