A sample of 100 people is selected for a survey, among the questions asked was"Do you like Statistics?" and "Do you live in Wollongong?". Of the 100 people, 80 said they like Statistics, 53 people said they like Statistics and also live in Wollongong(at the same time), 15 people said they don't like Statistics and also don't live in Wollongong (at the same time).a) Find the following probability, P(Likes Statistics | Live in Wollongong)b) Are the events "Likes Statistics" and "Lives in Wollongong" statistically independent?
Question
A sample of 100 people is selected for a survey, among the questions asked was"Do you like Statistics?" and "Do you live in Wollongong?". Of the 100 people, 80 said they like Statistics, 53 people said they like Statistics and also live in Wollongong(at the same time), 15 people said they don't like Statistics and also don't live in Wollongong (at the same time).a) Find the following probability, P(Likes Statistics | Live in Wollongong)b) Are the events "Likes Statistics" and "Lives in Wollongong" statistically independent?
Solution
a) The probability P(Likes Statistics | Live in Wollongong) is calculated as the number of people who like Statistics and live in Wollongong divided by the total number of people who live in Wollongong.
From the question, we know that 53 people like Statistics and live in Wollongong. However, we don't know the total number of people who live in Wollongong. We can find this by adding the people who like Statistics and live in Wollongong (53 people) to the people who don't like Statistics and don't live in Wollongong (15 people). This gives us a total of 68 people who live in Wollongong.
Therefore, P(Likes Statistics | Live in Wollongong) = 53 / 68 = 0.779 (rounded to three decimal places).
b) Two events are statistically independent if the occurrence of one does not affect the probability of the occurrence of the other. In this case, we can check this by comparing P(Likes Statistics) with P(Likes Statistics | Live in Wollongong).
We know that P(Likes Statistics) = 80 / 100 = 0.8. We have already calculated P(Likes Statistics | Live in Wollongong) as 0.779.
Since these two probabilities are not equal, the events "Likes Statistics" and "Lives in Wollongong" are not statistically independent.
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