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.

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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) About Me  (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 0.95%5E15 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 0.95%5E14%2A0.05 chance that will happen. And 0.9514*0.05 is about a 2.44% chance. And since those 14 trees can be picked in %28matrix%282%2C1%2C15%2C14%29%29 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%5E13%2A%280.05%29%5E2 chance that the first place 13 trees will live. There are %28matrix%282%2C1%2C15%2C13%29%29=105 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.