Error$-$correcting code $($ECC$)$ RAM is essential for servers because it prevents soft errors from occurring.

Soft errors occur when the bits stored in a computer's RAM suddenly flip unexpectedly. For example,

alpha particles emitted during radioactive decay or even cosmic rays cause bit flips by altering the

state of the RAM.

During the May $2003$ elections in Belgium in May $2003,$ a bit flips was suspected of causing extra votes

favoring a candidate.

In the $90\text{'}$s IBM estimated that in a month, one bit flip occurs for every $256$ MB of RAM. If a simulation

needs $32$ GB of RAM to run for $15$ days, what is the probability that at least one bit flip will occur

while the simulation is running?