SOLUTION: Trees planted by a landscaping firm have a 95% one-year survival rate, If they plant 15 trees in a park, what is the following probabilities: 1. All the trees survive one year.

Question 1157708: Trees planted by a landscaping firm have a 95% one-year survival rate, If they plant 15 trees in a park,
what is the following probabilities:
1. All the trees survive one year.
2. At least 13 trees survive one year.

Answer by Shin123(626) (Show Source): You can put this solution on YOUR website!
1. Since each tree has a 95% chance of lasting one year, there is a chance that all the trees will last. And 0.95¹⁵ 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 first 14 trees will last. There is a chance that will happen. And 0.95¹⁴*0.05 is about a 2.44% chance. And since those 14 trees can be picked in 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 chance that the first place 13 trees will live. There are ways for the 13 trees to be picked so there is a 0.95¹³*0.05²*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.
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