Comparing two experiments to predict the better chance
About this video
Nina compares two claw machines: Lucky Llama gave a prize 4 out of 5 times and Treasure Tiger 8 out of 15 times. Comparing the fraction of attempts that won (12/15 versus 8/15), not the number of prizes, shows Lucky Llama gives the better chance, though luck or skill could have affected the results.
You'll be able to
- compare chances from two experiments using fractions, not raw counts.
- rewrite fractions with a common denominator to compare them.
- explain why observed results don't guarantee future outcomes.
Key words
- attempt
- One try at something, like one turn on a claw machine.
- fraction of attempts
- The number of successes divided by the total number of tries.
- common denominator
- The same bottom number in two fractions, which makes them easy to compare.
Transcript
- [Instructor] We're told Nina is at an arcade and wants to win a stuffed animal from a claw machine. She records the results of people playing two different claw machines, so on the Lucky Llama machine, or it says the Lucky Llama machine awarded a prize four out of five times.
The Treasure Tiger machine awarded a prize eight out of 15 times. Nina gets one turn to play and wants the best chance of winning a prize. Based on these results, which machine gives Nina a better chance of winning a prize? Pause this video and have a go at that before we do this together.
Okay, so we're gonna look at this data, and there's a lot of things we don't know. Maybe the person using the Lucky Llama machine was more or less skilled at using the claw than the Treasure Tiger, but since we don't know any of that information, we'll just assume that that's all equal, and all we can go off of is the data.
Now, if you just looked at the absolute number of times that someone won a prize, you might be tempted to say, "Hey, look, Treasure Tiger, eight prizes versus four prizes. Maybe the Treasure Tiger's better," but you have to remember, it's eight out of 15. There were a lot more attempts here, three times more attempts for Treasure Tiger than for Lucky Llama, so if you really wanted to get a sense of which machine has a better chance, you really wanna look at the fraction of the attempts that resulted in a prize, and for Lucky Llama, it was four wins out of five attempts, while for Treasure Tiger, it was eight wins out of 15 attempts, and if you wanted to compare these directly, four out of five is the same thing
as if you multiply the denominator by three, you also have to multiply the numerator by three. It's the same thing as 12 out of 15, so if you just compared 12 out of 15 to eight out of 15, you'd say 12 out of 15 is better. This looks like a better chance, so just based on that, I would say that the Lucky Llama machine is better.
Now, you have to take all of this with a grain of salt, because this is just what you happen to observe. It might just be that the person who is using Treasure Tiger, or the people who are using Treasure Tiger, were just unlucky, or maybe the people who were using Lucky Llama were particularly lucky or particularly skilled at using a claw machine, so you don't know for sure whether Nina's decision to go with Lucky Llama is going to be better, but based on the information I just saw, four out of five is definitely a higher ratio or a higher fraction of the attempts that resulted in a prize than eight out of 15.
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