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. what is the probability of choosing a person at random who is a junior and plays video games? are these independent events? the p(junior and video games) = 32%; the two events are independent the p(junior and video games) = 32%, the two events are not independent the p(junior and video games) = 26%; the two events are independent the p(junior and video games) = 26%, the two events are not independent

Explanation:

Step1: Calculate probability of junior and video - games

The number of juniors who play video games is 48, and the total number of people surveyed is 150. The probability $P(\text{junior and video games})$ is $\frac{48}{150}=0.32 = 32\%$.

Step2: Check for independence

Let $A$ be the event of being a junior and $B$ be the event of playing video - games.
The probability of being a junior $P(A)=\frac{48 + 12}{150}=\frac{60}{150}=0.4$.
The probability of playing video - games $P(B)=\frac{48+45 + 6}{150}=\frac{99}{150}=0.66$.
$P(A)\times P(B)=0.4\times0.66 = 0.264
eq0.32$. So the two events are not independent.

Answer:

The $P(\text{junior and video games}) = 32\%$, the two events are not independent.