The monthly worldwide average number of airplane crashes of commercial airlines is 3.5. What is the probability that there will be

# The monthly worldwide average number of airplane crashes of commercial airlines is 3.5. What is the probability that there will be

H
240 points

The monthly worldwide average number of airplane crashes of commercial airlines is 3.5. What is the probability that there will be
(a) at least 2 such accidents in the next month;
(b) at most 1 accident in the next month?

The monthly
hansel

8.7k points

These circumstances fit a Poisson distribution,

$$P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}$$

with

$$\lambda = 3.5$$

worldwide monthly crashes

part (a)

$$P(\text{at least 2 such accidents})=1-P(\text{0 or 1 crashes})$$

$$=1-\frac{3.5^0 e^{-3.5}}{0!}-\frac{3.5^1 e^{-3.5}}{1!}\approx0.8641$$

part (b)

this is just the complement of part (a) or

$$1-0.8641=0.1359$$

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