Question

aditi downloads ten paid apps and sixteen free apps on her tablet. fourteen of them are game apps, and she paid for five of the game apps.
complete the statements to determine if the events \paid\ and \game\ are independent.
p(paid) =
p(paid | g
the even and \game\ are not independent.

Explanation:

Step1: Calculate total number of apps

Total apps = Paid apps + Free apps = \(10 + 16=26\)

Step2: Calculate \(P(\text{paid})\)

\(P(\text{paid})=\frac{\text{Number of paid apps}}{\text{Total number of apps}}=\frac{10}{26}\)

Step3: Calculate \(P(\text{paid}|\text{game})\)

Given \(P(\text{paid}|\text{game})=\frac{5}{14}\) (from problem statement)

Step4: Check independence

Two events \(A\) (paid) and \(B\) (game) are independent if \(P(A)=P(A|B)\). Here \(P(\text{paid})=\frac{10}{26}\approx0.385\) and \(P(\text{paid}|\text{game})=\frac{5}{14}\approx0.357\). Since \(\frac{10}{26}
eq\frac{5}{14}\), the events are not independent.

Answer:

\(P(\text{paid})=\frac{10}{26}\), \(P(\text{paid}|\text{game})=\frac{5}{14}\), the events “paid” and “game” are not independent.