Question

Trees planted by a landscaping firm have a 90% one-year survival rate, If they plant 16 trees in a park, what is the following probabilities:

(a) All the trees survive one year.
(b) At least 14 trees survive one year.

Answer 1

Pr(all will survive in one year) = 0.35 to 2 decimal places

Pr(at least 8 will survive) = 0.39 to 2 decimal places.

Explanation:

Probability of a tree surviving one year is 0.9. While not surviving probability is 1 - 0.9 = 0.1

This is obtained from the 90℅ surviving rate for one year planted by the landscaping firm.

Probability that if 10 trees are planted, all will survive for one year is:

0.9x0.9x0.9x0.9x0.9x0.9x0.9x0.9x0.9x0.9 = 0.9^10 = 0.349

Probability that at least 8 will survive in one year can be expressed as

8 survived x 2 not survived +(or) 9 survived x 1 not survived +(or) 10 survived

= [(0.9^8)x(0.1^2) + (0.9^9)x(0.1^1) + (0.9^10)] = 0.391

Explanation: