Video: Deciding If a Spinner Is Biased

Scarlett had a spinner with ten equal sections labeled with the numbers 1 to 10. She spun it 300 times and recorded the outcomes in a frequency table. If the spinner was fair, how many times would you expect to see each number if you spun it 300 times? State whether the spinner is biased and why.

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Video Transcript

Scarlett had a spinner with 10 equal sections labelled with the numbers one to 10. She spun it 300 times and recorded the outcomes in a frequency table. If the spinner was fair, how many times would you expect to see each number if you spun it 300 times?

An experiment is deemed to be fair if all outcomes are equally likely; that is to say, all outcomes have an equal probability or an equal chance of occurring. For this spinner, there are 10 possible outcomes. We know that the sum of the probabilities of these outcomes must be one. For the spinner to be fair then, each outcome must have a probability of one-tenth, or 0.1.

Once we know this, we can work out the number of times we would expect to see each number if the spinner was spun 300 times. Since each number has a probability of occurring of one-tenth and it’s spun 300 times, we can work out the expected number of times it should land on each number by multiplying one-tenth by 300. One-tenth multiplied by 300 is 30, so we would expect the spinner to land on each number 30 times.

State whether the spinner is biased and why.

In probability theory, a biased experiment is the opposite of a fair experiment. In a biased experiment, some outcomes are more likely to occur than others. If we look carefully at our table, we can see that most of the numbers occur somewhere close or around 30 times. However, four only occurs 11 times and nine occurs 49 times.

We can say then that it is a biased spinner because the number four occurs less than half of the number of times we would expect for a fair spinner and nine occurs much more often than we would expect.