a.An oil exploration firm is formed with enough capital to finance eleven explorations. Assume the probability of a particular exploration being successful is . Assume the explorations are independent. Find the probability that

i.exactly 2 explorations are not successful.

ii.at most 2 explorations are not successful.

iii.at least 3 explorations are successful.

iv.between 4 and 7 explorations are successful.

Evaluate the mean and the standard deviation of the distribution.