Advanced level maths.

[Ans:1 A satellite relies on solar cells for its power and will operate provided that at least one of the cells is working. Cells fail independently of each other, and the probability that an individual cell fails within one year is 0.8. (a) For a satellite with ten solar cells, find the probability that all ten cells fail within one year. b) For a satellite with ten solar cells, find the probability that the satellite is still operating at the end of one year. (c) For a satellite with n solar cells, write down the probability that the satellite is still operating at the end of one year. Hence, find the smallest number of solar cells required so that the probability of the satellite still operating at the end of one year is at least 0.95