<u>Answer:</u>
<em>Probability that the surgery is successful for exactly 6 patients is 0.088.</em>
<u>Step-by-step explanation:</u>
<em>The total number of patients is 10 and the probability of success is 0.8.</em>
We have to determine the probability of success of the surgery of exactly 6 patients.
<em>6 patients can be selected from 10 patients in
ways.</em>
<em>
</em>
<em>
</em>
<em>
</em>
<em>=210</em>
Let us consider a combination SSSSSSFFFF where S denotes success and F denotes failure. The probability of this combination is given by
<em>
since the chance of success is 0.8 and chance of failure is 0.2.</em>
There are 210 such different combinations possible and the probability of every combination is the same. So we have to sum up all the probabilities to determine the final probability.
<em>Therefore the probability that surgery is successful for 6 patients is
</em>