I get very confused when asked these types of questions. I need someone to explain it to me easier. Looking for another way to try to learn these questions.
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.
Isn't your name spelt Lucy?
I take it you're trying to teach me how to spell my name that I have had for 37 years!
I'd rather you, or someone else try to help me do this question!!! I'm not looking for the answer, just and EXPLANATION on how to do it!!! In future please don't bother people who are simply trying to understand things a little better. This is frustrating enough as it is.
LUCI
To answer these questions, we need to understand the concept of probability and apply it to the given information.
(a) To find the probability that Taiwan will experience four typhoons in a period of three months of the cyclone season, we can use the binomial probability formula.
The formula to find the probability of exactly k successes in n trials is:
P(k) = (nCk) * p^k * (1-p)^(n-k)
Where:
- nCk represents the number of combinations, which can be calculated as n! / (k! * (n-k)!).
- p is the probability of success for each trial.
In this case, the probability of experiencing a typhoon in any given month is the same throughout the season, so we can consider p = 3.6/5 (3.6 typhoons per season divided by 5 months).
Using this information, let's calculate the probability:
P(4) = (3C4) * (3.6/5)^4 * (1 - 3.6/5)^(3-4)
= 0
The probability of Taiwan experiencing exactly four typhoons in a period of three months is 0, which means it is not possible.
(b) To find the probability that Taiwan will experience at least five typhoons in a period of four months of the cyclone season, we need to calculate the probabilities for five, six, seven, and so on, up to the maximum possible number of typhoons in four months.
Using the same binomial probability formula, we can calculate each individual probability for these cases and then sum them up.
Let's calculate the probabilities and sum them:
P(at least 5) = P(5) + P(6) + P(7) + ... + P(maximum possible typhoons)
For simplicity, let's assume the maximum possible typhoons in four months is 4 (because the typhoon season lasts for five months).
P(at least 5) = P(5) + P(6) + P(7) + P(8)
The probability for each of these cases can be calculated using the binomial probability formula as shown in part (a).
(c) To determine if the number of typhoons per season is decreasing based on the 2014 season where Taiwan experienced only two typhoons, we cannot draw a definitive conclusion.
The data from a single season is not sufficient evidence to determine a trend or make a generalized statement about the number of typhoons per season. To analyze trends, you would need data from multiple seasons, preferably collected over a longer time span.