JEE Main · 2006 · 30 Apr 2006 · Offline · Probability

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At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10-minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is

(A) $\frac{6}{5 ^{e}}$
(B) $\frac{5}{6}$
(C) $\frac{6}{55}$
(D) $\frac{6}{e ^{5}}$ ✓ Correct

Answer: (D)

Solution

The number of calls follows a Poisson law with mean

m = 5

per ten-minute interval, so

P (X = r) = \frac{e ^{- 5} 5 ^{r}}{r !}

. The phrase at most one call means

P (X \leq 1) = P (X = 0) + P (X = 1) = \frac{e ^{- 5} 5 ^{0}}{0 !} + \frac{e ^{- 5} 5 ^{1}}{1 !} = e^{- 5} + 5 e^{- 5} = 6 e^{- 5}

, which is

\frac{6}{e ^{5}}

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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