In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.
Let M be the event that a student studies Mathematics and B be the event that a student studies Biology. From the problem, we are given the probabilities in terms of percentages: P(M) = 40% = 0.40, P(B) = 30% = 0.30, and P(M and B) = 10% = 0.10.
To find the probability that a student studies Mathematics or Biology, we use the addition theorem of probability. The formula is P(M or B) = P(M) + P(B) – P(M and B). This formula is necessary because simply adding P(M) and P(B) would count the students studying both subjects twice.
Substituting the given values into the formula: P(M or B) = 0.40 + 0.30 – 0.10 P(M or B) = 0.60. Therefore, the probability that the selected student is studying Mathematics or Biology is 0.60.
Explanation
This question tests the application of the addition theorem of probability, similar to Question 17 in the provided context. The context shows that to find P(A or B), one must account for the intersection P(A and B). The percentages are converted to probabilities (decimals or fractions) for calculation.
Solution Steps
Step 1: Define events and convert percentages to probabilities. P(M) = 40/100 = 0.40, P(B) = 30/100 = 0.30, P(M and B) = 10/100 = 0.10.
Step 2: Apply the addition theorem formula: P(M or B) = P(M) + P(B) - P(M and B).
Step 3: Substitute values: P(M or B) = 0.40 + 0.30 - 0.10.
Step 4: Calculate final result: P(M or B) = 0.60.