Question

1. A group of 80 people were asked if they liked different fruit, 38 said they liked apples, 42 like bananas, 10 of the people who liked cherries also liked bananas, 6 people like cherries and apples.

1. Venn Diagram showing this information.
2. How many people liked apples and bananas but did not like cherries ?
3. How many people liked none of the fruit ?
4. How many people liked just one of the fruit ?
5. How many people liked at least 2 of the fruits

Answer 1

I'm assuming you meant "group." Draw your 3 circles for apples, bananas, and cherries with overlap of all three with each other and make sure there is overlap between each two circles as well. Note your total = 38 + 42 + 14 = 94 (necessary to calculate the probability) is greater than the 80 people surveyed. Unfortunately, I cannot draw it here for you.

There does appear to be a problem with the total number of those who like cherries, as well. It can't be 14 with the overlap with other fruit likes, so check the number again. Even if I were to assume the 6 that like all 3 fruits included, for example, those that like apples and bananas (meaning those that strictly like apples and bananas = 20 - 6 = 14), my total using this approach would be 64, not 80.

After verifying the question, to find those that simply like one fruit, subtract the numbers that overlap from the total (using your original data, you should get 6 people like only apples, and 6 like only bananas). So the probability of those who like either apples or bananas would be 6 + 6 / 94 (or 12 / 94) if the numbers were correct for the cherry fans.