I don't know to calculate the answer of this question, please write down all steps. Thanks.

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A student opens 5 box (a, b, c, d, e) for many times.

There are some rules of box.

box a : can be opened 3 times. If there is no bomb in the box, you can get 25 coins. Otherwise, you will lose 16 coins. The probability of having a bomb is 0.23 .

box b: can be opened 10 times. If there is no bomb in the box, you can get 39 coins. Otherwise, you will lose 18 coins. The probability of having a bomb is 0.24 .

box c: can be opened 30 times. If there is no bomb in the box, you can get 11 coins. Otherwise, you will lose 5 times of opening the box. The probability of having a bomb is 0.12 .

box d: can be opened 34 times. If there is no bomb in the box, you can get 51 coins. Otherwise, you will lose 9 times of opening the box. The probability of having a bomb is 0.37 .

box e: can be opened 14 times. If there is no bomb in the box, you can get 13 coins. Otherwise, you will lose 13 coins. The probability of having a bomb is 0.35 .

Finally, he opens 50 times.

Question: What is the maximum expected number of coins? (might be float numbers)

Answer : The maximum coins he gets is 85.68

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How to calculate 85.68?