GATE Overflow Test Series | Probability | Test 1 | Question: 15

Question

Suppose that on a given weekend the number of accidents at a certain intersection has a poisson distribution with mean $0.6.$ The probability that there will be at least three accidents in the intersection during the weekend in percentage is _____ (Upto one decimal point)

Answer 1

Let $X$ denote the number of accidents that happen during the weekend.

$P(X \geq 3) = 1 -  P(X <  3)$

$\qquad = 1- P(X = 0) - P(X = 1) - P(X = 2) $

$\qquad =1  - e^{-0.6} - 0.6\times e^{-0.6} - 0.6^2 \frac{e^{-0.6}}{2}$

$\qquad= 2.31 \% $

Comments

Mean is given for the weekend & probability is also asked for weekend → No convertion → Just apply basic formula : 1 – P(0) – P(1) – P(2) = 2.31%

Answer 2

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