5 independent traffic lights, how many is car expected to pass without getting stoppedThere are 5 independent traffic lights, each with chance of stopping a car equal to 0.6. How many traffic lights is the car expected to pass before being stopped - what is E(X)?

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Zechariah Zavala · Accepted Answer

Step 1The change of passing no traffic lights at is 0.6The chance of passing exactly 1 traffic light is: 0.4⋅0.6 - that because we have to pass the first light and stop at the second.Following the same line, the chance of passing exactly 2 traffic lights is: 0.42⋅0.6The spacial case is passing exactly 5 lights which is 0.45 (we have no chance of passing new lights after that).Step 2So, summing it all, we have:   E  (  X  )  =  5  ⋅      0.4    5    +      ∑          n      =      0              4        n  ⋅      0.4    n    ⋅  0.6  =  0.65984

There are 5 independent traffic lights, each with chance of stopping a car equal to 0.6. How many traffic lights is the car expected to pass before being stopped - what is E(X)?

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