Explanation
Step 1: Understand the core definitions of Set Theory
Let the total percentage of students be represented by the universal set:
Total Students=100%
Let us define the events using set notation:
Percentage of students who passed Maths = P(M)=25%
Percentage of students who passed Science = P(S)=30%
Students who passed at least one subject means they passed Maths, Science, or both. This represents the union of the two sets: P(M∪S).
Step 2: Utilize the complement rule
The problem states that 10% of the students failed both subjects. This means these students do not belong to the passing sets of either Maths or Science.
In terms of logical sets, failing both is the exact complement of passing at least one:
Percentage who failed both=10%
According to probability and set principles:
P(Passed at least one)=Total Students−P(Failed both)
Substitute our known percentage values into the formula:
P(M∪S)=100%−10%
P(M∪S)=90%
