Question 1157708
1. Since each tree has a 95% chance of lasting one year, there is a {{{0.95^15}}} chance that all the trees will last. And 0.95<sup>15</sup> is equal to about 46.33% chance.
2.We need to find the probability that 13,14 or 15 trees last. In 1, we computed that there is a 46.33% chance that all 15 trees will last. Suppose we want to find the probability that the <b>first</b> 14 trees will last. There is a {{{0.95^14*0.05}}} chance that will happen. And 0.95<sup>14</sup>*0.05 is about a 2.44% chance. And since those 14 trees can be picked in {{{(matrix(2,1,15,14))}}} or 15 ways, there is a about 36.58%, if you don't round when you calculate to 2.44% and you round after. For 13 trees, there is {{{0.95^13*(0.05)^2}}} chance that the first place 13 trees will live. There are {{{(matrix(2,1,15,13))=105}}} ways for the 13 trees to be picked so there is a 0.95<sup>13</sup>*0.05<sup>2</sup>*105 chance which is about a 13.48% chance. So adding all the probabilities up, there is a 46.33%+36.58%+13.48%=96.39% chance that at least 13 trees survive.