Question

a survey of 167 persons was conducted at tcc, and it was found that 35 persons carried a cell phone, 90 persons carried a tablet computer, and 5 carried both a cell phone and a tablet.

1. how many people carried a cell phone or a tablet?

1. how many people carried neither a cell phone nor a tablet?

1. how many people carried a cell phone only?

1. how many people carried a tablet but not a cell phone?

Explanation:

Step1: Define given values

Let $n(U)=167$ (total surveyed), $n(C)=35$ (cell phone carriers), $n(T)=90$ (tablet carriers), $n(C\cap T)=5$ (carried both).

Step2: Calculate "cell phone or tablet"

Use the principle of inclusion-exclusion:
$$n(C\cup T)=n(C)+n(T)-n(C\cap T)$$
$$n(C\cup T)=35+90-5=120$$

Step3: Calculate "neither device"

Subtract $n(C\cup T)$ from total surveyed:
$$n(\text{neither})=n(U)-n(C\cup T)$$
$$n(\text{neither})=167-120=47$$

Step4: Calculate "cell phone only"

Subtract those with both from cell phone carriers:
$$n(C\text{ only})=n(C)-n(C\cap T)$$
$$n(C\text{ only})=35-5=30$$

Step5: Calculate "tablet but not cell phone"

Subtract those with both from tablet carriers:
$$n(T\text{ only})=n(T)-n(C\cap T)$$
$$n(T\text{ only})=90-5=85$$

Answer:

1. 120
2. 47
3. 30
4. 85