Beacon Hill Trees & Shrubs currently has an inventory of 10 fruit trees, 8 pine trees, and 14 maple trees. It plans to give 4 trees away at next Saturday's lawn and garden show in the city park. The 4 winners can select which type of tree they want. Assume they select randomly. What is the probability that 3 winners will select pine trees and the other tree will be a maple?
A) 0.0058
B) 0.0218
C) 0.0355
D) 0.0709

Question

Quizplus · Accepted Answer

The probability of 3 winners selecting pine trees and 1 selecting a maple tree can be calculated using combinations and the basic probability formula. There are a total of 32 trees (10 fruit + 8 pine + 14 maple). The probability of this specific selection is calculated as follows:- The number of ways to choose 3 pine trees out of 8 is $ \binom{8}{3} $.- The number of ways to choose 1 maple tree out of 14 is $ \binom{14}{1} $.- The total number of ways to choose any 4 trees out of 32 is $ \binom{32}{4} $.The probability is then:$$ P = \frac{\binom{8}{3} \times \binom{14}{1}}{\binom{32}{4}} $$Calculating the values:$$ P = \frac{56 \times 14}{35960} = \frac{784}{35960} \approx 0.0218 $$Therefore, the correct answer is 0.0218, which corresponds to choice B.

Beacon Hill Trees & Shrubs Currently Has an Inventory of 10