SOLUTION: Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wire
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-> SOLUTION: Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wire
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Question 1164269: Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter.
If four neighbors with the same type of opener set their switches independently, what is the probability of at least one pair of neighbors using the same settings? Answer by ikleyn(52884) (Show Source):
Wording seems to be complicated, but the problem is, actually, quite simple.
With 4 switches, each of which can be in any of the two possible positions,
there are = 16 different setting for the control.
So, the probability for every one single of 4 neighbors to have the same setting in his (or her) control is
(their controls are of the same construction (!) ).
The probability that NO ONE of 4 neighbors has the same setting is .
The probability under the question is the COMPLEMENT to it, i.e.
P = 1 - = 1 - 0.7225 = 0.2275. ANSWER
Solved.
Very nice probability problem (!)
Hope that I correctly use the technical terms in my post . . .
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