Posted by **andrew** on Friday, November 3, 2006 at 9:54am.

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

*multiply* the probabilities. To find out if either one or another of events will occur, you

*add* 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

**^2**
That is p squared.

Sorry for the omission.

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