Question

A survey of 150 people at a local high school about playing video games was conducted, and the results are posted in the table.Play Video GamesDo Not Play Video GamesJuniors4812Seniors4525Teachers614What is the probability of choosing a person at random who is a teacher and plays video games? Are these independent events?

Answer 1

The number of surveyed teachers who play videogames is 6, according to the table; therefore,

`P(Teacher\cap Videogames)=(6)/(150)=(1)/(25)=0.04=4\%`

On the other hand, if A and B are two independent events,

`\begin{gathered} A,B\rightarrow\text{ independent events} \\ \Rightarrow P(A\cap B)=P(A)P(B) \end{gathered}`

Thus, in our case,

`\begin{gathered} P(Teacher)P(Videogames)=(6+14)/(150)*(48+45+6)/(150)=(20)/(150)*(99)/(150)=(11)/(125)=0.088 \\ \Rightarrow P(Teacher\cap Videogames)\\e P(Teacher)P(Videogames) \end{gathered}`

Therefore, the two events are not independent.

Hence, the answer is the first option, 4%, and not independent.