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I have a circuit, in order for it to work the electricity has to travel from point $A$ to point $B$, but on its way there it encounters $4$ independent switches. If any one of them is closed the system will function properly. the probability of a switch being closed is $.3$ for all $4$ switches, what is the overall probability that the system functions.

Currently I tried using a tree diagram but that offered me no help and quickly just made it more confusing. im not sure where to even begin or what to start with

JKnecht
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noahdukeh
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2 Answers2

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For problems like this, solve the probability that the system will fail. Then subtract that number from 1 to get the probability it will not fail.

For it to fail, all switches would have to fail. That probability would be $${0.7}^4$$

Subtract that from 1 to get your answer.

Your tree diagram would also work. It would need to be 4 tiers. You would find that all paths work except for the path where all 4 switches failed. The sum of the 15 other paths is found the same way I detailed above.

turkeyhundt
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  • I understood "open" to mean "fail" and OP only needed one to be closed to function (parallel). I could be wrong though. – turkeyhundt Jan 29 '16 at 01:25
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You want to find the probability of at least 1 switch being closed. An easy way to do this is to find the probability that all the switches aren't closed are take the complement. $P(\mbox{All switches are open})=(.7)^4=0.2401$. Thus, $P(\mbox{At least one switch is closed})=1-0.2401=0.7599$

Jürgen Sukumaran
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