Probability
Classical Probability
Grade 12
Question:
<p><strong>For Problems 4–6:</strong> In an objective paper, there are two sections of 10 questions each. For 'section 1', each question has 5 options and only one option is correct and 'section 2' has 4 options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in 'section 1' is 1 and in 'section 2' is 3. (There is no negative marking.)</p><p>If a candidate attempts only two questions by guessing, one from 'section 1' and one from 'section 2', the probability that he scores in both questions is</p>
<p>(1) 74/75</p>
<p>(2) 1/25</p>
<p>(3) 1/15</p>
<p>(4) 1/75</p>
Step-by-Step Solution
Key Concept: The candidate must get BOTH questions correct simultaneously. For Section 1 (single correct answer): probability = 1/5. For Section 2 (multiple correct answers): must identify ALL correct options from 4 options, with probability = 1/2^4 = 1/16 (since each option is independently correct or incorrect). Multiply these independent probabilities.
<p><strong>Step 1: Analyze Section 1 (single correct answer, 5 options)</strong></p><p>Probability of guessing correctly = 1/5</p><p><strong>Step 2: Analyze Section 2 (multiple correct answers, 4 options)</strong></p><p>For each of the 4 options, the candidate must decide: correct or incorrect. When guessing, there are 2^4 = 16 equally likely outcomes. Only 1 outcome matches the actual set of correct answers. Probability of guessing all correct answers = 1/16</p><p><strong>Step 3: Find probability of scoring in BOTH questions</strong></p><p>Since the two attempts are independent:</p><p>P(both correct) = P(Section 1 correct) × P(Section 2 correct)</p><p>P(both correct) = (1/5) × (1/16) = 1/80</p><p>∴ Answer: D</p>
Correct Answer: D