The probability that a randomly selected individual in a country earns more than 75,000 per is 10.5%. the probability that a randomly selected individual in a country earns more than 75,000 per year, given that the individual has earned a bacholer’s degree is 21.5%. The events are “earned more than 75,000” and “earned a bacholer’s degree”. Are these events independent?
In order to determine whether the events "earned more than $75,000" and "earned a bachelor's degree" are independent, we need to compare the conditional probability to the marginal probability.
Let's denote:
A = "earned more than $75,000"
B = "earned a bachelor's degree"
We are given the following probabilities:
P(A) = 0.105 (probability of earning more than $75,000)
P(A|B) = 0.215 (probability of earning more than $75,000 given a bachelor's degree)
If the events are independent, then P(A|B) should be equal to P(A), meaning that the probability of earning more than $75,000 would be the same regardless of having a bachelor's degree or not.
To verify this, we compare the conditional probability P(A|B) to the marginal probability P(A).
P(A|B) = 0.215
P(A) = 0.105
Since P(A|B) does not equal P(A), we can conclude that the events "earned more than $75,000" and "earned a bachelor's degree" are not independent.
To determine if the events "earned more than $75,000" and "earned a bachelor's degree" are independent, we need to compare the probability of one event happening regardless of the occurrence of the other event, with the probability of one event happening given that the other event has already occurred.
Let's represent the two events as follows:
A = earned more than $75,000
B = earned a bachelor's degree
If the events are independent, then the probability of A happening should be the same regardless of whether B has occurred or not. Mathematically, we would expect P(A) = P(A|B).
Given the information provided:
P(A) = 10.5% = 0.105
P(A|B) = 21.5% = 0.215
Since P(A|B) ≠ P(A), we can conclude that the events "earned more than $75,000" and "earned a bachelor's degree" are dependent, meaning that having a bachelor's degree affects the probability of earning more than $75,000 per year in this country.
In summary, the events "earned more than $75,000" and "earned a bachelor's degree" are not independent based on the given probabilities.
Ty
B=bachelor's degree
H=high income
P(H)=0.105
P(H|B)
=P(H∩B)/P(B)
=0.215
=>
P(H∩B)=P(H|B)*P(B)
=0.215*0.105
>0
So H and B are not independent.