Probability
Basic Probability
Grade 12
Question:
<p>In a class of 125 students 70 passed in Mathematics, 55 in Statistics, and 30 in both. Then find the probability that a student selected at random from the class has passed in only one subject.</p>
Step-by-Step Solution
Key Concept: Use set theory to find students who passed exactly one subject: those in M only plus those in S only, which equals (M - both) + (S - both). Then divide by total to get probability.
<p><strong>Step 1:</strong> Identify given information</p><p>Total students = 125</p><p>Passed Mathematics (M) = 70</p><p>Passed Statistics (S) = 55</p><p>Passed both (M ∩ S) = 30</p><p><strong>Step 2:</strong> Find students who passed ONLY Mathematics</p><p>Students in M only = M - (M ∩ S) = 70 - 30 = 40</p><p><strong>Step 3:</strong> Find students who passed ONLY Statistics</p><p>Students in S only = S - (M ∩ S) = 55 - 30 = 25</p><p><strong>Step 4:</strong> Find students who passed exactly one subject</p><p>Students passing only one subject = 40 + 25 = 65</p><p><strong>Step 5:</strong> Calculate probability</p><p>P(passed only one subject) = 65/125 = 13/25</p><p><strong>∴ Answer: 13/25</strong></p>
Correct Answer: 13/25