Question

A group of 100 customers in a restaurant are asked which frults they like from a choice of mangoes, bananas and kiwi fruits. The results are as follows. a) 15 like all three fruits. b) 22 like mangoes and bananas. c) 33 like mangoes and kiwi fruits. d) 27 like bananas and kiwi fruits. e) 8 like none of these three fruits. f) x like only mangoes

Answer 1

The question is a high school level mathematics problem involving probabilities and survey data interpretation to find out how many people prefer only mangoes.

Step-by-step explanation:

The subject in question here is Mathematics, specifically the subset area involving probability and combinations, as well as the interpretation of survey data. The context provided suggests that this is most likely a high school level question. To approach this question, one would need to construct a Venn diagram to represent the different categories of fruit preferences among the 100 customers and use it to solve for the unknown variable 'x', which represents the number of people who like only mangoes. The information provided includes the number of people who like different combinations of the three fruits and the number who like none. Given that some people may like only one or two types of fruit, others may like all three, or none, the goal is to find out what portion fits exclusively into the mango-only category.

Answer 2

The total number of customers who like only one type of fruit is 11.

a) 15 like all three fruits.

b) 22 like mangoes and bananas.

c) 33 like mangoes and kiwi fruits.

d) 27 like bananas and kiwi fruits.

e) 8 like none of these three fruits.

Let's denote: (M) as the number of customers who like only mangoes.(B) as the number of customers who like only bananas.

(K) as the number of customers who like only kiwi fruits.

The total number of customers is 100.

Using the Principle of Inclusion-Exclusion: [M + B + K - (a + b + c + d) + e = 100.]

Substituting the given values: [M + B + K - (15 + 22 + 33 + 27) + 8 = 100.][M + B + K = 100 - 15 - 22 - 33 - 27 + 8 = 11.]

Complete question :-

A group of 100 customers in a restaurant are asked which fruits they like from a choice of mangoes, bananas and kiwi fruits. The results are as follows.

15 like all three fruits
22 like mangoes and bananas
33 like mangoes and kiwi fruits
27 like bananas and kiwi fruits
8 like none of these three fruits
x like only mangoes

b. The number of customers that like only mangoes is equal to the number of customers that like only kiwi fruits. This number is half of the number of customers that like only bananas. Complete your Venn diagram from part (a) with this additional information in terms of z.