Question

In a survey it is to be found that 70% of employees like bananas and 64% like apples. If x% like both bananas and apples, then

A. x≥34
B. x≤64
C. 34≤x≤64
D. all of these

Answer 1

The question involves finding the bounds for the percentage of employees who like both bananas and apples, given the percentages who like each. The principle of inclusion and exclusion in probability yields that the percentage liking both must be between 34% and 64%. Therefore, the answer is C. 34≤x≤64.

Step-by-step explanation:

The question pertains to the concept of set theory in probability. Specifically, it deals with understanding the bounds of the percentage of employees who like both bananas and apples based on given percentages of those who like each fruit individually.

Using the principle of inclusion and exclusion, we can determine that the maximum percentage (x) of people who like both is the percentage of people who like apples, which is 64%. Therefore, x cannot be more than 64. This sets the upper bound for x.

The minimum percentage (x) of people who like both can be calculated by summing the percentages of those who like each fruit and subtracting 100%, because the total cannot exceed 100%. So, the minimum percentage is 70% + 64% - 100% = 34%. This sets the lower bound for x.

From this, we can conclude that the value of x must be such that 34% ≤ x ≤ 64%. Thus, the correct answer is C. 34≤x≤64.