Daily Math Puzzle: 2026-04-07
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2026-04-07
InnovateNow, a budding tech startup, is days away from its app launch. A critical bug has been discovered which, if not addressed, carries a 50% chance of causing a total system crash during the launch. Their lead developer brings in a freelance expert who proposes two strategies, but only one can be chosen: 1. **Direct Fix:** Attempt to fix the bug itself. This strategy has a 75% chance of completely eliminating the bug and thus the crash risk. If it fails (25% chance), the bug remains and still carries the original 50% crash risk. 2. **Workaround:** Implement a complex workaround that, if successful, will prevent the crash even if the bug persists. This strategy has an 80% chance of success. If it fails (20% chance), the workaround provides no protection, and the bug still carries the original 50% crash risk. Which strategy should InnovateNow choose to minimize the probability of a system crash during launch?
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Solution
Workaround — Let P(C) be the initial probability of a system crash, which is 50% (0.50).
**Strategy 1: Direct Fix**
* If the fix is successful (75% chance or 0.75), the crash risk becomes 0%. So, P(C | Fix Success) = 0.
* If the fix fails (25% chance or 0.25), the bug remains, and the original 50% crash risk persists. So, P(C | Fix Failure) = 0.50.
The overall probability of a crash with Strategy 1 is calculated as:
(Probability of Fix Success * P(C | Fix Success)) + (Probability of Fix Failure * P(C | Fix Failure))
= (0.75 * 0) + (0.25 * 0.50)
= 0 + 0.125
= 0.125 or 12.5%
**Strategy 2: Workaround**
* If the workaround is successful (80% chance or 0.80), it prevents the crash, making the crash risk 0%. So, P(C | Workaround Success) = 0.
* If the workaround fails (20% chance or 0.20), it provides no protection, and the original 50% crash risk persists. So, P(C | Workaround Failure) = 0.50.
The overall probability of a crash with Strategy 2 is calculated as:
(Probability of Workaround Success * P(C | Workaround Success)) + (Probability of Workaround Failure * P(C | Workaround Failure))
= (0.80 * 0) + (0.20 * 0.50)
= 0 + 0.10
= 0.10 or 10%
Comparing the two strategies, Strategy 2 (Workaround) results in a lower probability of a system crash (10%) than Strategy 1 (Direct Fix) (12.5%). Therefore, InnovateNow should choose the Workaround.
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