Notice the shared gate

Separate independent components from routes that share a bottleneck, then compare two upgrades.

Follow every required component

Each numbered component works independently with the chance shown inside it. Plain connecting lines always work. A complete route needs every numbered component along it to work.

Both routes in this layout use component 1. The upper route then uses component 2; the lower route uses component 3. If component 1 fails, neither route can connect start to finish. The components are independent, but the two complete routes share a state.

A shared gate before two alternatives
11/221/231/2StartFinish

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First lesson in this subject: Count equally likely outcomes

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