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?
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To calculate the probabilities, we can use the rules of probability theory. Let's break down each question step by step:
1. What is the chance that Magneto A OR Magneto B will fail?
To find the chance that either Magneto A or Magneto B will fail, we need to calculate the probability of both magnetos NOT failing and then subtract it from 1.
Since the probability of one magneto failing is 1 in 1000, the probability of both magnetos NOT failing can be calculated as:
P(A not failing) = 1 - (1/1000) = 999/1000
P(B not failing) = 1 - (1/1000) = 999/1000
To find the probability that either Magneto A or Magneto B fails, we can take the complement of both magnetos not failing:
P(A or B fail) = 1 - P(A not failing) * P(B not failing)
Using the probabilities stated above:
P(A or B fail) = 1 - (999/1000) * (999/1000)
2. What is the chance that Magneto A AND Magneto B will fail?
To find the chance that both Magneto A and Magneto B will fail, we simply multiply their individual failure probabilities:
P(A and B fail) = (1/1000) * (1/1000) = 1/1,000,000
3. What is the chance that Magneto A NOR Magneto B will fail?
The phrase "A nor B" refers to the situation where neither Magneto A nor Magneto B fails. This can be calculated by taking the product of the probabilities of both magnetos not failing:
P(A nor B fail) = P(A not failing) * P(B not failing) = (999/1000) * (999/1000)
So, to recap:
1. The chance that Magneto A OR Magneto B will fail is 1 - (999/1000) * (999/1000).
2. The chance that Magneto A AND Magneto B will fail is (1/1000) * (1/1000).
3. The chance that Magneto A NOR Magneto B will fail is (999/1000) * (999/1000).