3E Rory, Elisha and Harry each spun the same spinner a number of times and recorded how many times it landed on a section labelled 5. Their results are shown below. a) They each used their own results to work out the estimated probability of the spinner landing on 5 . Which person had the best estimate for the probability? b) By combining all of their results, work out the estimated probability of the spinner landing on 5 Give your answer as a decimal. c) Will using the combined results give a better or worse estimate than using only one person's results? Write a sentence to explain your answer.

Question

3E Rory, Elisha and Harry each spun the same spinner a number of times and recorded how many times it landed on a section labelled 5. Their results are shown below. a) They each used their own results to work out the estimated probability of the spinner landing on 5 . Which person had the best estimate for the probability? b) By combining all of their results, work out the estimated probability of the spinner landing on 5 Give your answer as a decimal. c) Will using the combined results give a better or worse estimate than using only one person's results? Write a sentence to explain your answer.

Answer 1

a) Elisha had the best estimate for the probability with a P of

.b) Combined, the estimated probability results to P

when pared down.c) Using combined results gives a better estimate because according to the Law of Large Numbers, a higher number of experiments gets us closer to the true probability.

Answer 2

## Step 1: Calculate the estimated probability of spinner landing on 5 for each person. The formula for probability is:###

For each person, the probability of landing on 5 could be calculated as:

## Step 2: Determine who has the highest probability estimate:By examining the results, the highest probability is:Elisha with Probability

## Step 3: Combining all results, calculating the combined probability of spinner landing on 5:The combined results could be calculated by adding up all the number of spins and the times it landed on the number 5. Here's how it would look like:

## Step 4: Understanding the better estimate.Taking into consideration the Law of Large Numbers (LLN), which in probability theory suggests that the result of performing the same experiment a large number of times would yield to an outcome expected to be the probabilistic expected outcome, aggregating all given data will give a more accurate estimate for a simple reason: as you increase the number of experiments (spins in this particular case), your result tends toward the expected value. In this case, more data equals more spins; the more spins, the closer we theoretically get to the true probability.

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