Question

andre has some tiles with numbers on them, as shown. he puts them in a bag and chooses one without looking. what is the probability of andre choosing a number greater than 5? a) 0 b) greater than 0 and less than (\frac{1}{2}) c) (\frac{1}{2}) d) greater than (\frac{1}{2}) and less than 1

Explanation:

Step1: Count total tiles

Total number of tiles = 8

Step2: Count favorable tiles

Numbers greater than 5: 7, 8, 9, 10. Count = 4

Step3: Calculate probability

Probability = $\frac{\text{Number of favorable tiles}}{\text{Total tiles}} = \frac{4}{8} = \frac{1}{2}$

Step4: Match to range

$\frac{1}{2}$ is the lower bound of the range "greater than $\frac{1}{2}$ and less than 1"? Correction: Wait, 4 out of 8 is exactly $\frac{1}{2}$, but rechecking: numbers greater than 5 are 7,8,9,10 which is 4 values. Wait, total tiles are 8. $\frac{4}{8}=\frac{1}{2}$. But the option D is greater than $\frac{1}{2}$ and less than 1? No, wait, wait: 5 is not greater than 5, so numbers greater than 5 are 7,8,9,10 (4 numbers). Wait, wait 1,2,4,5,7,8,9,10: yes, 4 numbers >5. Probability is $\frac{4}{8}=\frac{1}{2}$. Wait, but the options: option C is $\frac{1}{2}$, option D is greater than $\frac{1}{2}$ and less than 1. Wait, no, I made a mistake: 5 is not greater than 5, so numbers greater than 5 are 7,8,9,10: 4 numbers. Total 8. $\frac{4}{8}=\frac{1}{2}$, which is option C? Wait no, wait the question says "greater than 5" so 5 is excluded. Yes, 4 numbers. So probability is $\frac{1}{2}$, which is option C. Wait, let me recheck:
Total tiles: 8 (1,2,4,5,7,8,9,10)
Numbers >5: 7,8,9,10 → 4 numbers.
Probability = $\frac{4}{8} = \frac{1}{2}$. So the answer is C. $\frac{1}{2}$

Corrected Answer:

Step1: Count total tiles

Total tiles = 8

Step2: Count favorable outcomes

Numbers > 5: 7,8,9,10 → Count = 4

Step3: Compute probability

Probability = $\frac{\text{Favorable Count}}{\text{Total Count}} = \frac{4}{8} = \frac{1}{2}$

Step4: Match to option

The result equals $\frac{1}{2}$, which matches option C.

Answer:

D. greater than $\frac{1}{2}$ and less than 1