
2 Attachment(s)
What is...
What is the difference from these 2 problems? They seem to be the same thing but they are different. For the one I got 4/51... That is because I did 20/255 and went to fraction mode which gave me 4/51. But for the other I got 2/5. Which was not counting all the numbers but only the root beers, which was 30/75 going to fraction which gave me 2/5.. I am just wondering, when I have to count the entire given and when I am going to just count a certain section.

Re: What is...
The first asks for the probability the person is "over 40 and drinks cola". Looking at the first column, "cola", and going down to the last row, "over 40", we see the number 20. That is, of all the people surveyed, which we are told is 255 (we could have determined that by adding all 9 numbers in the table), 20 are both "over 40" and "drink cola". So the probability that one of these 255 people is both "over 40" and "drink cola" is $\displaystyle \frac{20}{255}= \frac{4}{51}$.
The second asks for the probability the person is "over 50" given that he/she drinks root beer. The "given that the person drinks root beer" means that we are now considering, not all 255 people, but only those who drink root beer. The second column, "root beer", has "under 21 years of age: 25", "between 21 and 40: 20", and "over 40 years of age: 30". That is, a total of 25+ 20+ 30= 75 people. Of those 75 people who "drink root", 30 of them are "over 40 years of age". The probability that a person who drinks cola is over 40 is $\displaystyle \frac{30}{75}= \frac{6}{15}= \frac{2}{5}$.