Your town holds an annual fun fair. This year there is an intriguing offer at the basketball stand:

“For a $5 entry fee, you are given a basketball and one of two options:

1. One Shot to Score

2. Two out of Three Shots to Score

If you succeed, you are given $20.”

As you have been practicing hard over the school holidays, you decide to pay the $5 entry fee to play this game. According to your mom, you are the next Michael Jordan. And whilst she does exaggerate (sometimes), you estimate that you make 6 out of every 10 shots.

And thus after paying, the fun fair man asks you

“Which option would you like, sir / madam?”

Answer

If you make an estimated 60% of your shots, it is better to take the second bet. The follow up question is. Which success rate ( % of shots made) will make you switch bets. There is an algebraic formula to work this one out. If you figure it out, leave it in the comments section.

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