Jerry starts at 0 on the real number line. He tosses a fair coin 8 times. When he gets heads, he...

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Jerry starts at 0 on the real number line. He tosses a fair coin 8 times. When he gets heads, he moves 1 unit in the positive direction; when he get tails, he moves 1 unit in the negative direction. The probability that he reaches 4 at some time during this process \( a / b \), where \( a \) and \( b \) are relatively prime positive integers. What is \( a+b \) ? (For example, he succeeds if his sequence of tosses is \( \mathrm{HTHHHHHH} \) ).
(a) 69
(b) 151
(c) 257
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