In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both English and Hindi. If a student is selected at random, what is the probability that the student has offered English or Hindi (or both)?

Introduction / Context:
This question tests the use of set theory within probability, specifically the inclusion exclusion principle for two sets, English and Hindi. We are given percentage data for students offering English, Hindi and both, and asked to find the probability that a randomly chosen student has offered at least one of the two subjects.

Given Data / Assumptions:

• P(English) = 30% = 0.30.
• P(Hindi) = 20% = 0.20.
• P(English and Hindi) = 10% = 0.10.
• We assume percentages are based on the same total number of students.
• We want P(English or Hindi).

Concept / Approach:
For two events E and H, the probability of E or H is given by P(E or H) = P(E) + P(H) minus P(E and H). The minus term removes the double counting of students who offered both subjects. After computing the probability as a decimal, we convert it into a simplified fraction for the final answer.

Step-by-Step Solution:
P(English) = 0.30. P(Hindi) = 0.20. P(English and Hindi) = 0.10. P(English or Hindi) = P(English) + P(Hindi) - P(English and Hindi). P(English or Hindi) = 0.30 + 0.20 - 0.10 = 0.40. 0.40 as a fraction is 40 / 100 = 2 / 5.

Verification / Alternative check:
Imagine a class of 100 students. Then 30 offered English, 20 offered Hindi and 10 are counted in both subject groups. So total students who offered at least one of the two subjects = 30 + 20 - 10 = 40. The probability is therefore 40/100 = 2/5, consistent with the earlier calculation.

Why Other Options Are Wrong:
1/2 represents 50%, which would require 50 students in 100 offering at least one subject, not 40. 3/4 (75%) and 4/5 (80%) are much larger than the computed 40%, so they are clearly incorrect.

Common Pitfalls:
A frequent mistake is to simply add 30% and 20% and conclude 50% without subtracting the 10% who are counted twice. Forgetting the overlap overestimates the probability. Always apply the inclusion exclusion formula for unions of sets.

Final Answer:
Thus, the probability that a randomly chosen student has offered English or Hindi is 2/5.