I don't know how to begin this question and it is due tonight. I'm not looking for someone to give me the answer. I just need help with the formula that I use and how do I go about answering this?
Is the formula:
P = P(total subject) / P(OJ drinker over 40)
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
255/30 = .118
To answer the question, you need to determine the probability that a randomly chosen subject prefers orange juice given they are over 40.
To calculate this probability, you need to use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, A represents the event that the person prefers orange juice, and B represents the event that the person is over 40.
So, to calculate P(A and B), you need to find the number of subjects that prefer orange juice and are over 40, and divide it by the total number of subjects.
From the given information, you can see that there are 30 subjects who prefer orange juice and are over 40. Since there are a total of 255 subjects, you have:
P(A and B) = 30 / 255
Now, you need to calculate P(B), which represents the probability of a subject being over 40. From the information provided, you can see that there are 20 subjects who are in the "Over 40 years" category. Therefore:
P(B) = 20 / 255
Plugging these values into the formula, you have:
P(A|B) = (30 / 255) / (20 / 255)
Simplifying this expression, you can cancel out the denominator:
P(A|B) = (30 / 20)
Calculating this, you get:
P(A|B) = 1.5
The probability that a randomly chosen subject prefers orange juice, given they are over 40, is 1.5.
However, it's worth mentioning that this result seems to be greater than 1, which is not a valid probability. It's possible that there was an error in the given data or in the way in which the problem was presented. Double-checking the numbers and the problem statement may help clarify the issue.