Final answer:
The probability that all three valves will leak within one year of installation is calculated by multiplying the independent probabilities of each valve leaking, resulting in a 2.7% chance when rounded to one decimal place.
Step-by-step explanation:
To calculate the probability that all three valves will leak within one year of installation, you would multiply the probability of each valve leaking independently as they are separate events. Given that each valve has a 30% chance of leaking, we represent this as 0.30. The calculation for all three valves leaking is 0.30 (for the first valve) × 0.30 (for the second valve) × 0.30 (for the third valve).
The calculation is as follows:
0.30 × 0.30 × 0.30 = 0.027
As a percentage, this is 0.027 × 100, which equals 2.7%. Therefore, the probability that all three valves will leak within one year of installation is 2.7% when rounded to one decimal place.