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Fill chance across regimes

ProbabilityEasy

A resting order fills with chance $90%$ in a busy session, $60%$ in a normal session and $20%$ in a quiet one. Today is busy with chance $40%$ , normal with chance $35%$ and quiet with chance $25%$ . What is the chance the order fills today? Give a decimal.

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Hint

Weight each session's fill chance by the chance of that session.

Solution

Busy sessions contribute $0.4 \times 0.9 = 0.36$ , normal ones $0.35 \times 0.6 = 0.21$ , and quiet ones $0.25 \times 0.2 = 0.05$ .
The total is $0.36 + 0.21 + 0.05 = 0.62$ .

Answer: $0.62$

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