Probability
Basic Probability
Grade 12
Question:
<p>In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is:</p>
<p>\(\dfrac{1}{6}\)</p>
<p>\(\dfrac{1}{3}\)</p>
<p>\(\dfrac{2}{3}\)</p>
<p>\(\dfrac{5}{6}\)</p>
Step-by-Step Solution
Key Concept: Use the complement principle with set theory: find total students who opted for at least one activity, then subtract from total to get students with neither. Apply P(neither) = n(neither)/total.
<p><strong>Step 1:</strong> Apply inclusion-exclusion to find students who opted for at least one activity.</p><p>n(NCC ∪ NSS) = n(NCC) + n(NSS) - n(NCC ∩ NSS)</p><p>n(NCC ∪ NSS) = 40 + 30 - 20 = 50</p><p><strong>Step 2:</strong> Find students who opted for neither activity.</p><p>n(neither) = Total - n(NCC ∪ NSS) = 60 - 50 = 10</p><p><strong>Step 3:</strong> Calculate the probability.</p><p>P(neither) = n(neither)/Total = 10/60 = 1/6</p><p>∴ Answer: <strong>1/6</strong></p>
Correct Answer: A