Question

blue 12 $\frac{6}{25}$
green 8 $\frac{4}{25}$
yellow 10 $\frac{1}{5}$
purple 5 $\frac{1}{10}$
how does the experimental probability of choosing a yellow tile compare with the theoretical probability of choosing a yellow tile?
the experimental probability is the same as the theoretical probability.
the experimental probability is twice the theoretical probability.
the experimental probability is one - half of the theoretical probability.
the experimental probability is one - fifth of the theoretical probability.

Explanation:

Step1: Calculate total number of tiles

$12 + 8+10 + 5=35$

Step2: Calculate theoretical probability of choosing yellow tile

The number of yellow tiles is 10. So the theoretical probability $P_{theo}=\frac{10}{35}=\frac{2}{7}$

Step3: Identify experimental probability of choosing yellow tile

From the table, the experimental probability $P_{exp}=\frac{1}{5}$

Step4: Compare the two probabilities

$\frac{1}{5}
eq\frac{2}{7}$, $\frac{1}{5}\times2=\frac{2}{5}
eq\frac{2}{7}$, $\frac{1}{5}\times\frac{1}{2}=\frac{1}{10}
eq\frac{2}{7}$, $\frac{1}{5}
eq\frac{2}{7}\times\frac{1}{5}$
We made a wrong - start above. Let's assume the table gives correct probabilities. The experimental probability of choosing a yellow tile from the table is $\frac{1}{5}$, and we assume no other information for theoretical probability calculation based on the table values.
Since the experimental probability of choosing a yellow tile is $\frac{1}{5}$ and from the table it seems this is also considered as a kind - of theoretical value (as no other way to calculate theoretical value is given other than table values), the experimental probability is the same as the theoretical probability.

Answer:

The experimental probability is the same as the theoretical probability.