A typhoon is a mature tropical cyclone that develops in the western part of the North Pacifi c Ocean
between 180� and 100� E. One of the countries a�ffected by typhoons is Taiwan. The typical typhoon season
in this country lasts from June to October and averages around 3.6 typhoons per season. For simplicity, we
assume the probability of arrival of a typhoon is the same for any given month of the season.
(a). What is the probability that Taiwan will experience four typhoons in a period of three months of the
cyclone season?
if the season is five months long how do you figure out this question? I'm very lost
(b). What is the probability that Taiwan will experience at least fi ve typhoons in a period of four months
of the cyclone season?
This is similar to (a) but over five months so I still don't gt it.
(c). In the season of 2014, Taiwan experienced only two typhoons (Matmo and Vongfong). Does it indicate
that the number of typhoons per season is decreasing? Support your answer by indicating a relevant
probability.
I would assume that there is not enough evidence to prove that the typhoons are decreasing each year as these figures are only for a period of one season.
I have revisited this question and this is what i've come up with....
get the average typhoons per month, so 3.6/5=0.72
then for part a. use the binomial coefficient equation????and then the same for b. just different numbers.
And then part c. has blown me away??
Some advice would be nice.
Can someone please help me out with this?????
Any hint would be great.
To solve part (a) of the question, we can use the binomial probability formula. Here's how you can calculate the probability that Taiwan will experience four typhoons in a period of three months of the cyclone season:
1. First, calculate the average number of typhoons per month. Given that the typical typhoon season lasts from June to October and averages around 3.6 typhoons per season, we divide 3.6 by 5 to get an average of 0.72 typhoons per month.
2. Since we want to find the probability of experiencing four typhoons in three months, we need to calculate the probability of getting four successes (typhoons) out of three trials (months).
3. Apply the binomial probability formula:
P(X = k) = C(n, k) * p^k * q^(n - k)
Where:
- P(X = k) is the probability of getting exactly k successes
- C(n, k) is the binomial coefficient, calculated as n! / (k! * (n - k)!)
- p is the probability of success in a single trial (0.72 in this case)
- q is the probability of failure in a single trial (1 - p)
- n is the number of trials (3 in this case)
- k is the number of successes (4 in this case)
Now you can calculate the probability of experiencing four typhoons in three months by substituting the values into the formula.
To solve part (b) of the question, you can follow a similar approach as in part (a), but now you will be calculating the probability of experiencing at least five typhoons in a period of four months. This means you need to calculate the probabilities for each possible number of successes (5, 6, 7, 8), and then add them up to get the probability of "at least five" typhoons.
As for part (c) of the question, you correctly pointed out that one season's observation is not enough to determine a long-term trend. To support your answer, you could calculate the probability of Taiwan experiencing only two typhoons in a season, assuming that the average is 3.6 typhoons per season. However, keep in mind that this calculation assumes a uniform distribution and does not consider other potential factors influencing typhoon occurrence, so it should be seen as a rough estimate rather than definite proof of a trend.
I hope this helps! Let me know if you have any further questions.