75 yards in northern Virginia have a sprinkler system. 80% of the yards with sprinklers are fertilized where 60% of yards without sprinklers are also fertilized.
1. In the space provide the missing values of A,B, and C ?
Step By Step Answers with Explanation
- 75 yards in northern Virginia have a sprinkler system.
To answer this question, we need to define some terms:
- A: The probability that a yard has a sprinkler.
- 60% of yards without sprinklers are fertilized, which means the probability of a yard not having a sprinkler and being fertilized is 0.60. Since A represents the probability of having a sprinkler and not having a sprinkler (complement), we can express this as A(1 - B) = 0.60.
Now, let's solve for A and B:
Now, we need to express C in terms of A and B, since C represents the probability of having a sprinkler and being fertilized:
C = A * B
A * B = 0.80
Now, we can isolate A from this equation:
0.80(1 - B) = 0.60B
0.80 - 0.80B = 0.60B
A = 0.80 / B
A ≈ 0.80 / 0.5714
C = 0.80
2. What is the volume that a randomly selected yard is fertilized?