I don't know where to start with this one. What is the formula and how do I go about answering this?
Question:
If one of the 255 subjects is randomly chosen, what is the probability that the person prefers orange juice, given they are over 40? Round your answer to 3 decimal places.
Water Orange Cola
juice
Under 21 years 40 25 20
21 – 40 years 35 20 30
Over 40 years 20 30 35
Assuming the central vertical value is OJ, 30/255.
There was no answer to check.
To answer this question, you need to use conditional probability. Conditional probability is the probability of an event occurring, given that another event has already occurred.
In this case, the event is that the person prefers orange juice and the condition is that they are over 40 years old. So, you need to find the probability of someone preferring orange juice among those who are over 40.
To calculate this probability, you will need to use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
Where:
P(A|B) is the probability of event A occurring given that event B has already occurred.
P(A and B) is the probability of both events A and B occurring.
P(B) is the probability of event B occurring.
In this case, event A is preferring orange juice and event B is being over 40 years old.
To find P(A and B), you need to find the number of subjects who prefer orange juice and are over 40. From the table, you can see that there are 30 subjects who prefer orange juice and are over 40.
To find P(B), you need to find the number of subjects who are over 40. From the table, you can see that there are 20 subjects who are over 40.
Now you can calculate the probability using the formula:
P(A|B) = P(A and B) / P(B) = 30/20 = 1.5
However, probabilities cannot be greater than 1, so the maximum probability would be 1. Therefore, you need to round the probability to 3 decimal places:
P(A|B) = 1.5 (rounded to 3 decimal places) = 1.000
So, the probability that a randomly chosen subject prefers orange juice, given they are over 40, is 1.000.