The Math Of Broken iPhones

Discrete Mathematics Level 2

In an iPhone, there are numerous crucial components like a circuit board, an antenna, a liquid crystal display (LCD), and a battery. Over time, these components will experience wear and tear, and the iPhone will start to malfunction if any of them fail. In this event, you would not know which component had failed, or even the number of components that failed. You can only reboot your phone and hope for the best.

If the iPhone has 20 crucial components, each of which independently has a \( 0.1 \% \) chance of failing within the first year after purchase, what is the percentage chance (in %) that the iPhone will malfunction in the first year?

Feel free to use a calculator, and round your answer to the nearest integer.

Image credit: Gary Booth

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