Question
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?
Answer
3.9
(269 Votes)
Gwawr
Master · Tutor for 5 years
Answer
The goal here is to estimate the number of pink counters in the bag.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. The raw data for this experiment is presented in the table as given:| Number of counters chosen | Number of pink counters chosen || ------------------------- | -------------------------------|| 2 | 1 || 5 | 1 || 50 | 11 || 100 | 14 || 200 | 24 |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).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:``` math\frac{24}{200} = \frac{p}{50}```Solving the above equivalent fractions equation for `p` gives us:``` mathp = \frac{24}{200}*50``` Hence, ``` mathp \approx 6```Therefore, the best estimate for the number of pink counters in the bag is around **6**.