You are given the task of testing a wireless link between Delhi and Hyderabad. You do so by

sending many bits $($each bit is either $0$ or $1)$ over the link from Delhi to Hyderabad. A receiver at Hyderabad

records, for every sent bit, its estimate $(0$ or $1)$ of what was sent. At the end of the experiment you come up

with the following data. You find that $90\%$ of the bits sent are received correctly. You also find that amongst the

correctly received bits, $70\%$ of the bits were sent as $1.$ Also, $30\%$ of the wrongly received bits were sent as $1.$

The cost of sending a bit that is correctly received is $100$ and that of sending a bit that is wrongly received is

$50.$ What is the expected cost of sending a bit over the link?