Explanation

(b)
$\because\ (0.99)^{15} = (1 - 0.01)^{15}$
$= 1 - \ ^{15}C_{1}(0.01) + \ ^{15}C_{2}{(0.01)}^{2} - \ ^{15}C_{3}{(0.01)}^{3} + ...$
We want to answer correct upto 4 decimal places and as such, we have left further expansion.
$= 1 - 15(0.01) + \frac{15 \bullet 14}{1 \bullet 2}(0.0001) - \frac{15 \bullet 14 \bullet 13}{1 \bullet 2 \bullet 3}(0.000001) + ...$
$= 1 - 0.15 + 0.0105 - 0.000455 + ...$
$= 1.0105 - 0.150455$
$= 0.8601$