which event has a probability greater than 0 and less than 1/2? choosing a tile with an even number choosing…

Explanation:

Step1: Calculate total number of tiles

There are 8 tiles.

Step2: Analyze "Choosing a tile with an even number"

Even - numbered tiles are 2, 6, 8, 10. So the number of favorable outcomes is 4. Probability $P_1=\frac{4}{8}=\frac{1}{2}$.

Step3: Analyze "Choosing a tile with a number greater than 6"

Numbers greater than 6 are 8, 9, 10. So the number of favorable outcomes is 3. Probability $P_2 = \frac{3}{8}$. Since $0<\frac{3}{8}<\frac{1}{2}$.

Step4: Analyze "Choosing a tile with the number 7"

There is no 7 - numbered tile. So the number of favorable outcomes is 0. Probability $P_3=0$.

Step5: Analyze "Choosing a tile with a number less than 9"

Numbers less than 9 are 1, 2, 3, 5, 6, 8. So the number of favorable outcomes is 6. Probability $P_4=\frac{6}{8}=\frac{3}{4}>\frac{1}{2}$.

Answer:

Choosing a tile with a number greater than 6