Probability
Basic Probability
Grade 12
Question:
<p>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.</p>
<p>(a) 0.5</p>
<p>(b) 0.6</p>
<p>(c) 0.65</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Apply the addition rule for probability: \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\) to avoid double-counting.
<p>Let M = event that student studies Mathematics, B = event that student studies Biology</p><p>Given: \(P(M) = 0.4\), \(P(B) = 0.3\), \(P(M \cap B) = 0.1\)</p><p>Using the addition rule: \(P(M \cup B) = P(M) + P(B) - P(M \cap B)\)</p><p>\(P(M \cup B) = 0.4 + 0.3 - 0.1 = 0.6\)</p>
Correct Answer: B