JEE MAIN - Mathematics (2006 - No. 12)
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 :
$${6 \over {{5^e}}}$$
$${5 \over 6}$$
$${6 \over 55}$$
$${6 \over {{e^5}}}$$
Explanation
Required probability
$$ = P(X = 0) + P(X = 1)$$
$$ = {{{e^{ - 5}}} \over {0!}}{5^0} + {{{e^{ - 5}}} \over {1!}}{5^1}$$
$$ = {e^{ - 5}} + 5{e^{ - 5}}$$
$$ = {6 \over {{e^5}}}$$
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