Question

abby had 50 counters in a bag.

she chose one at random, recorded whether or not it was blue, and then put it back in the bag.
she did this a total of 200 times.
the table below shows her results after different numbers of counters had been chosen.

what is the best estimate for the number of blue counters in the bag?

Explanation:

⚡ Using what you learned: experimental (empirical) probability

Step 1: Find the best probability estimate

To get the most reliable estimate of the probability of choosing a blue counter, we use the largest number of trials because a larger sample size reduces experimental error.

Using the data for \( 200 \) trials:

$$ P(\text{blue}) \approx \frac{24}{200} = 0.12 $$

Step 2: Calculate the expected number of blue counters

Multiply this probability by the total number of counters in the bag (\( 50 \)):

$$ \text{Estimated blue counters} = 50 \times 0.12 = 6 $$

Answer:

6