Question
Imagine a LONG bike with a total of 4 wheels - 2 in the front and 2 in the back.
For the bike to work at all, at least 1 front wheel and 1 back wheel must be operational.
All 4 tires are the same and each, individually, has probability 'p' of failing.
What is the probability that I will have a working bike? (meaning, that at least 1 tire is working up front, and at least 1 is working in the back).
When you want to know the probability that more than one probability will occur, you <I>multiply</I> the probabilities. To find out if either one or another of events will occur, you <I>add</I> the probabilities.
Thus you would use the following formula:
1 - (pF1 + pF2)(pR1 + pR2), where pF1 is the probability for one front tire failing.
However, since the probability is the same for each tire, the formula would be:
1 - (p + p)(p + p) = 1 - (2p)(2p) = 1 - 4p
I hope this helps. Thanks for asking.
Pardon my typo.
1 - (2p)(2p) = 1 - 4p<B>^2</B>
That is p squared.
Sorry for the omission.
For the bike to work at all, at least 1 front wheel and 1 back wheel must be operational.
All 4 tires are the same and each, individually, has probability 'p' of failing.
What is the probability that I will have a working bike? (meaning, that at least 1 tire is working up front, and at least 1 is working in the back).
When you want to know the probability that more than one probability will occur, you <I>multiply</I> the probabilities. To find out if either one or another of events will occur, you <I>add</I> the probabilities.
Thus you would use the following formula:
1 - (pF1 + pF2)(pR1 + pR2), where pF1 is the probability for one front tire failing.
However, since the probability is the same for each tire, the formula would be:
1 - (p + p)(p + p) = 1 - (2p)(2p) = 1 - 4p
I hope this helps. Thanks for asking.
Pardon my typo.
1 - (2p)(2p) = 1 - 4p<B>^2</B>
That is p squared.
Sorry for the omission.