Luke had 50 counters in a bag. He chose one at random, recorded whether or not it was pink, and then put it back in the bag. He did this a total of 200 times . The table below shows his results after different numbers of counters had been chosen. What is the best estimate for the number of pink counters in the bag?

<br />The goal here is to estimate the number of pink counters in the bag.<br /><br />Luke performed an experiment where he randomly picked one of 50 counters from a bag and then put the counter back in again. He recorded whether the counter chosen was pink or another not mentioned color. <br /><br />The raw data for this experiment is presented in the table as given:<br /><br /><br />| Number of counters chosen | Number of pink counters chosen |<br />| ------------------------- | -------------------------------|<br />| 2 | 1 |<br />| 5 | 1 |<br />| 50 | 11 |<br />| 100 | 14 |<br />| 200 | 24 |<br /><br /><br />We can observe from the "Number of pink counters chosen" in the right-most column that Luke picked a pink counter about 12% of the times he selected a counter from the bag (24 pink counters of the total 200 total counters).<br /><br />Let's denote `p` as the estimated number of pink counters in the bag. Since we're assuming that the proportion of times he got a pink counter is equivalent to the proportion of pink counters from the entire 50 counters, we can express this assumption mathematically as follows:<br /><br />``` math<br />\frac{24}{200} = \frac{p}{50}<br />```<br /><br />Solving the above equivalent fractions equation for `p` gives us:<br /><br />``` math<br />p = \frac{24}{200}*50<br />```<br /> <br />Hence,<br /> <br />``` math<br />p \approx 6<br />```<br /><br />Therefore, the best estimate for the number of pink counters in the bag is around **6**.