Question

An aircraft door has 3 components - a mechanical system and a hydraulic system, which need to work in tandem for the door to operate, and in case the above system fails, there is also an electronic controller which can operate the door all by itself. The chances that the mechanical system, the hydraulic system, and the electronic controller work properly are 90%, 80%, and 95% respectively. What is the probability that the door will be operational at any point in time?​

Answer 1

Answer:

It's not stated, but I'll assume that the chances of each component failing are independent.

The chance that both the mechanical and the hydraulic systems work is 72%. Therefore, the chance that at least one of them fails, preventing you from using that tandem to open the door, is 28%. The chance that the electronic system fails is 5%. Therefore, the chance that you can't open the door is 1.4% so the chance that you will be able to open the door is 0.986.

Step-by-step explanation:

Answer 2

Given,

The probability of the mechanical system working properly$\[ = 0.90\]$

The probability of the mechanical system working properly$\[ = 0.80\]$

The probability of the mechanical system working properly$\[ = 0.95\]$

To find,

The probability that the door will be operational at any point in time.

Solution,

Know that probability is defined as the numerical value of the happening of an event.

In the given question in order that the door opens all the systems i.e. the mechanical system, the hydraulic system, and the electronic controller work should properly.

Therefore,

$\[\begin{array}{l} \Rightarrow 0.90 \times 0.80 \times 0.95\\ \Rightarrow 0.684\\ \Rightarrow 68.4\% \end{array}\]$

Hence, the probability that the door will be operational at any point in time is$\[68.4\% \]$.