aditi downloads ten paid apps and sixteen free apps on her tablet. fourteen of them are game apps, and she…

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 | game) = the events “paid” and “game” are

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 | game) = the events “paid” and “game” are

Answer

Answer:

$P(\text{paid})=\frac{10}{10 + 16}=\frac{10}{26}=\frac{5}{13}$ $P(\text{paid}|\text{game})=\frac{5}{14}$ The events "paid" and "game" are not independent.

Explanation:

Step1: Calculate P(paid)

Total apps = $10+16 = 26$. Paid apps = 10. So $P(\text{paid})=\frac{\text{Number of paid apps}}{\text{Total number of apps}}=\frac{10}{26}=\frac{5}{13}$

Step2: Calculate P(paid|game)

There are 14 game - apps and 5 paid game - apps. So $P(\text{paid}|\text{game})=\frac{\text{Number of paid game apps}}{\text{Number of game apps}}=\frac{5}{14}$

Step3: Determine independence

For two events A and B to be independent, $P(A)=P(A|B)$. Here, $\frac{5}{13}\neq\frac{5}{14}$, so the events are not independent.