Question

A survey of 391 children given at a local elementary school showed that 150 like chocolate ice cream, 225 like pistachio ice cream, and 116 do not like chocolate or pistachio ice cream. How many children like at least one kind of ice cream mentioned in the survey? a) 125 b) 375 c) 275 d) 50 e) 175 f) None of the above.

Answer 1

Answer:275 children like at least, one ice cream

Explanation:

The Venn diagram is shown in the attached photo. Circle C represents the children that like chocolate ice cream. Circle P represents the children that like pistachio ice cream.

x represents the number of children that like both chocolate ice cream and pistachio ice cream.

From the Venn diagram, the number of children that like chocolate ice cream only is 150 - x

while the number of children that like pistachio ice cream only is 225 - x.

Total number of children is 391

Therefore

150 - x + x + 225 - x + 116 = 391

491 - x = 391

x = 491 - 391 = 100

Therefore the number of children that like at least one kind of ice cream would be

100 + (150 - 100) + (225 - 100)

= 100 + 50 + 125 = 275

Answer 2

275

Explanation:

Given that a survey of 391 children given at a local elementary school showed that 150 like chocolate ice cream, 225 like pistachio ice cream, and 116 do not like chocolate or pistachio ice cream.

Total = 391

cholocate ice cream =150

pistchio ice cream = 225

Neither -=116

If we partition universal set into disjoint sets exhaustive

we have A-B, B-A, AB, and (AUB)'

Total = 391

Let n(AB) i.e. likes both be x

Then we have n(A-B) = 150-x and n(B-A) = 225-x

Totalling

`150-x+225-x+x+116 =391\\491-x =391\\x =100`

no of children who like atleast one kind of ice cream = n(U)-n(AUB)"

= 391-116

= 275