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Patients arrive randomly and independently at a Doctor’s room from 8 AM at an average rate of one in 5 minutes. The waiting room can accommodate 12 persons. The probability that the room will be full when the doctor arrives at 9 AM is

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$\frac{e^{- 12} 12^{12}}{∠ 12}$

$\sum_{x = 0}^{11} \frac{e^{- 12} 12^{12}}{∠ x}$

$1 - \sum_{x = 0}^{11} \frac{e^{- 12} 12^{x}}{∠ x}$

$1 - \sum_{x = 0}^{\infty} \frac{e^{- 12} 12^{x}}{∠ x}$

answer is C.

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Detailed Solution

$λ = 12; The probability that the room will be full when the doctor arrives at 9 AM isP (X \geq 12) = 1 - \sum_{x = 0}^{x = 11} \frac{e^{- 12} 12^{x}}{x!}$

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