Probability
Binomial Distribution
Grade 12
Question:
<p>The probability that a bulb produced by a factory will fuse after 150 days if used is 0.50. What is the probability that out of 5 such bulbs none will fuse after 150 days of use?</p>
<p>(1) \(1 - (19/20)^5\)</p>
<p>(2) \((19/20)^5\)</p>
<p>(3) \((3/4)^5\)</p>
<p>(4) \(90 (1/4)^5\)</p>
Step-by-Step Solution
Key Concept: This is a binomial probability problem where each bulb independently has probability 0.50 of fusing. For none to fuse, all 5 must survive, which means each bulb must NOT fuse with probability 0.50.
<p><strong>Step 1:</strong> Identify the given information.</p><p>• Probability that a bulb will fuse after 150 days: P(fuse) = 0.50</p><p>• Probability that a bulb will NOT fuse: P(not fuse) = 1 - 0.50 = 0.50</p><p>• Number of bulbs: n = 5</p><p><strong>Step 2:</strong> For none of the 5 bulbs to fuse, each bulb must independently NOT fuse.</p><p>Since the bulbs operate independently:</p><p>P(none fuse) = P(bulb 1 doesn't fuse) × P(bulb 2 doesn't fuse) × ... × P(bulb 5 doesn't fuse)</p><p><strong>Step 3:</strong> Calculate the probability.</p><p>P(none fuse) = (0.50)^5 = (1/2)^5 = 1/32 ≈ 0.03125</p><p>∴ Answer: <strong>1/32 or 0.03125 (Option B)</strong></p>
Correct Answer: B