Discussion
An atom is restricted to move in one dimension by making unit jumps either to the left or right, as shown in the figure. Assuming that a jump to the left or right is equally probable, the probability of the atom returning back to the starting point after four jumps is
Answer: C
The probability is 0.375.
Four jumps of +1 or -1, each equally likely, give \(2^{4} = 16\) equally likely sequences. To return to 0 the atom needs two jumps right and two left, in any order:
\[ P = \frac{\binom{4}{2}}{2^{4}} = \frac{6}{16} = 0.375 \]
0.250 (4 of 16) and 0.500 (8 of 16) miscount the six favourable orderings, and 0.333 cannot arise at all, since every probability here is a whole number of sixteenths.
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