Probability
Classical Probability
Grade 12
Question:
<p>Four fair dices are thrown simultaneously. Find the probability that the highest number obtained is 4.</p>
<p>\(\dfrac{175}{1296}\)</p>
<p>\(\dfrac{125}{1296}\)</p>
<p>\(\dfrac{100}{1296}\)</p>
<p>\(\dfrac{150}{1296}\)</p>
Step-by-Step Solution
Key Concept: The highest number is 4 means all four dice show values ≤4, AND at least one die shows exactly 4. Use complementary counting: P(max=4) = P(all≤4) - P(all≤3).
<p><strong>Step 1:</strong> Find P(highest number ≤ 4)</p><p>All four dice must show values from {1,2,3,4}</p><p>P(all ≤ 4) = (4/6)⁴ = (2/3)⁴ = 16/81</p><p><strong>Step 2:</strong> Find P(highest number ≤ 3)</p><p>All four dice must show values from {1,2,3}</p><p>P(all ≤ 3) = (3/6)⁴ = (1/2)⁴ = 1/16</p><p><strong>Step 3:</strong> Calculate P(highest = 4)</p><p>P(max = 4) = P(all ≤ 4) - P(all ≤ 3)</p><p>= 16/81 - 1/16</p><p>= (256 - 81)/(81×16)</p><p>= 175/1296</p><p>∴ Answer: A</p>
Correct Answer: A