$2.$S$16$ WP Transactions to a computer database are either new items or changes to previous items. The addition of an item can be completed in less than $100$ milliseconds $90\%$ of the time, but only $20\%$ of changes to a previous item can be completed in less than this time. If $30\%$ of transactions are changes, what is the probability that a transaction can be completed in less than $100$ milliseconds?