Question

A survey of 117 consumers found that 81 had a tablet computer, 70 had

a smartphone and 29 had both a smartphone and a tablet computer. Find the number of consumers surveyed who have neither a
smartphone nor a tablet.

Answer 1

Explanation:

If we call A the group that has a tablet computer and B the group that has a smartphone. In this case we can apply a formula that tells us that:

# (AUB) = #A + #B - #AnB - NoANoB

We know all these values except the one that has neither A nor B.

# (AUB) = the number of respondents, that is 117.

#A = The number of people who have a tablet, that is 81.

#B = The number of people who have a smarphone, that is, 70.

#AnB = intersection of both groups, that is, they have both, that is 29.

Replacing:

117 = 81 + 70 - 29 - NoANoB

NoANoB = 81 + 70 - 29 - 117

NoANoB = 5

Which means that 5 people have neither a tablet nor a smartphone.

Answer 2

5

Explanation:

If we call A the group that has a tablet computer and B the group that has a smartphone. In this case we can apply a formula that tells us that:

# (AUB) = #A + #B - #AnB - NoANoB

We know all these values except the one that has neither A nor B.

# (AUB) = the number of respondents, that is 117.

#A = The number of people who have a tablet, that is 81.

#B = The number of people who have a smarphone, that is, 70.

#AnB = intersection of both groups, that is, they have both, that is 29.

Replacing:

117 = 81 + 70 - 29 - NoANoB

NoANoB = 81 + 70 - 29 - 117

NoANoB = 5

Which means that 5 people have neither a tablet nor a smartphone.