From a statistical point of view, you have three options.
Don't make the second jump and go home with $10,000. Make the second jump, fail, and go home with $5,000. Make the second jump, succeed, and go home with $20,000.
If you make the second jump, you'll earn an average of $12,500. Furthermore, this isn't a null-sum game; if you you fail, you still leave with more than you came with. There's no losing scenario, unless you lose your lunch.
Meanwhile, if you really found bungee jumping so terrifying, you wouldn't have made the first jump -- after one successful jump with an almost-successful break, the second jump surely won't be as scary as the first.
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Don't make the second jump and go home with $10,000.
Make the second jump, fail, and go home with $5,000.
Make the second jump, succeed, and go home with $20,000.
If you make the second jump, you'll earn an average of $12,500. Furthermore, this isn't a null-sum game; if you you fail, you still leave with more than you came with. There's no losing scenario, unless you lose your lunch.
Meanwhile, if you really found bungee jumping so terrifying, you wouldn't have made the first jump -- after one successful jump with an almost-successful break, the second jump surely won't be as scary as the first.