varaderiyw
2021-11-18
There are 3.5 commercial airliner aircraft crashes on average each month around the world. What is the likelihood that (a) there will be at least two of these accidents in the upcoming month; (b) there will only be one accident in the upcoming month? Describe your thinking!
Phisecome
Beginner2021-11-19Added 18 answers
An average of 3.5 aircraft crashes occur per month. We must determine the likelihood that at least two accidents of this nature will occur in the upcoming month. Let n represent the number of monthly flights. Of course n is big. Also let be a Bernoulli random variable where represents a probability that a plane will crash. Obviously
The binomial distribution is approximated by a Poisson distribution since n is very high (the number of flights is supposed to be large) and we may assume that the likelihood of crash is very tiny (it is evident). Consequently, a random variable
where . We need to calculate . Let's remember that if .
It follows:
In the (b) part we are calculating the porbability of at most 1 accident happening. Similar as before we have:
We calculate the probability for the (a) part, which is 0.86 and for the (b) part, which is 0.136.
Sarythe
Beginner2021-11-20Added 11 answers
Step-by-step explanation:
We would apply the formula for poisson distribution which is expressed as
Where
r represents the number of successes of the event.
From the information given,
a)
For the probability that there will be at least 2 such accidents in the next month, it is expressed as
Therefore,
b)
For the probability that there will be at most 1 accident in the next month, it is expressed as
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