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
Asked by 3 years ago
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?
Explain your reasoning!

The monthly
hansel

1 Answer

Answered by 3 years ago
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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Views: 44
Asked: 3 years ago

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