I have an airplane that has an ignition system that works like this. There are 2 energy producing devices, called magnetos that "fire" the spark plugs, 2 per cylinder. There is a 1 in a 1000 chance that one will fail.

What is the chance that Magneto A OR Magneto B will fail?
What is the chance that Magneto A AND Magneto B will fail?
What is the chance that Magneto A NOR Magneto B will fail?

To calculate the probabilities, we need to understand the concepts of "OR," "AND," and "NOR" in probability calculations.

1. To find the chance of Magneto A OR Magneto B failing, we use the concept of "OR" probability. The formula is:

P(A OR B) = P(A) + P(B) - P(A AND B)

Given that there is a 1 in 1000 chance of one magneto failing, we calculate:

P(A OR B) = (1/1000) + (1/1000) - (1/1000 * 1/1000)

Simplifying the equation:

P(A OR B) = 2/1000 - 1/1000000

Therefore, the chance that either Magneto A or Magneto B will fail is 2/1000 - 1/1000000.

2. To find the chance of Magneto A AND Magneto B failing, we use the concept of "AND" probability. The formula is:

P(A AND B) = P(A) * P(B)

Given that there is a 1 in 1000 chance of one magneto failing, we calculate:

P(A AND B) = (1/1000) * (1/1000)

Simplifying the equation:

P(A AND B) = 1/1000000

Therefore, the chance that both Magneto A and Magneto B will fail is 1/1000000.

3. To find the chance of Magneto A NOR Magneto B failing, we use the concept of "NOR" probability. The formula is:

P(A NOR B) = 1 - P(A OR B)

Given that we have already calculated P(A OR B) as 2/1000 - 1/1000000, we can calculate:

P(A NOR B) = 1 - (2/1000 - 1/1000000)

Simplifying the equation:

P(A NOR B) = 1 - 2/1000 + 1/1000000

Therefore, the chance that neither Magneto A nor Magneto B will fail is 1 - 2/1000 + 1/1000000.