Question

A poll of 500 people determines that 382 like ice cream and 362 like cake. How many people like both if each of them likes at least one of the two?

Answer 1

284 people like both.

Explanation:

In order to solve this you just have to use the next formula:

b.= p(a) + p(b) − p(a)

We just have to insert the values into the formula:

B=382+362-500

B=784-500

B=284

So the number of people that like both ice cream and cake, is 284.

Answer 2

244

Explanation:

Given data:

People liking ice cream, P(A) = 382

People liking cake, P(B) = 362

Total people, P(A∪B) = 500

Now,

We know,

P(A∪B) = P(A) + P(B) - P(A∩B)

where,

P(A∩B) = People liking both the ice cream and the cake

On substituting the respective values, we get

500 = 382 + 362 - P(A∩B)

or

P(A∩B) = 244

Hence,

the number of people who like both ice cream and the cake are 244