Question

Suppose that 80% of students have a cell phone and 70% have cable TV. Moreover, 2/3 of students with a cell phone or cable TV, have both a cell phone and a cable TV. What is the percentage of students that do not have a cell phone and do not have a cable TV?

Answer 1

Ans:

P(cell phone)=0.8

P(cable TV)=0.7

P(cell phone and cable TV)=(2/3)*P(cell phone or cable TV)

Now,

P(cell phone or cable TV)=P(cell hone)+P(cable TV)-P(cell phone and cable TV)

P(cell phone or cable TV)=0.8+0.7-(2/3)*P(cell phone or cable TV)

(5/3)P(cell phone or cable TV)=1.5

P(cell phone or cable TV)=1.5*3/5=0.9

Now,

P(neither cell phone nor cable TV)=1-0.9=0.1 or 10%

So, 10% of students that do not have a cell phone and do not have a cable TV.