When things are operating$$ properly, a certain Internet bank can process a maximum of $37$ electronic transfers every minute during the busiest periods of the day. If it receives more transfer requests than$$ this, then the$$ bank's computer system will become so overburdened that it will slow to the point that no electronic transfers can be handled. If during the busiest periods of the day requests for electronic transfers arrive at the rate of $240$ per$10-$minute period on$$ average, what is the probability that the system will be overwhelmed by$$ requests? Assume that the process can be described using a Poisson distribution.

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Part $1$

The probability that the system will be overwhelmed by requests is

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