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!
Happy Learning!
The Daily Challenge Team
