Why does cross multiplying work because he didn't actually say much about why? And in the basketball story, I still don't get why your average goes up
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[Originally posted in Discussions]
Why does cross multiplying work because he didn't actually say much about why? And in the basketball story, I still don't get why your average goes up because even though you made a shot, the total number of shots you attempted also goes up. Is it that the additional shot made outweighs the negative impacts of attempting another shot overall?
And also in the basketball story, isn't it that no matter how many shots you make after you miss a few, you will never have a perfect average?
Cross-multiplying has the effect of making the denominators (the bottoms) of the fractions the same. This makes it easy to see which fraction is bigger, because you only need to compare the numerators (the top numbers). If you look back to the video at 1:07, you will see the explanation of why.
When you make one shot, your average goes up slightly; the increase is small if you have already made a lot of shots. If you made only one shot and failed the first time, your average would be 0%, and making a success shot at that point would bring your average to 1/2, or 50%, which is the largest possible increase in your average. Intuitively, it makes sense that your average should go up, because you are getting better at making basketball shots.
Yes, you are absolutely right that you cannot achieve a 100% success rate, no matter how many shots you make!
I hope this helps! Please ask if you have any more questions!
The Daily Challenge Team