Garage Door Opener Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with six independent switches, each one set on or off. The receiver ( wired to the door ) must he set with the same pattern as the transmitter. ( Exercises 71-74 are based on ideas similar to those of the “birthday problem” in the For Further Thought feature in this section. ) If five 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? (Give your answer to four decimal places.)
Garage Door Opener Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with six independent switches, each one set on or off. The receiver ( wired to the door ) must he set with the same pattern as the transmitter. ( Exercises 71-74 are based on ideas similar to those of the “birthday problem” in the For Further Thought feature in this section. ) If five 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? (Give your answer to four decimal places.)
Solution Summary: The author calculates the probability of at least one pair of neighbours using the same settings provided there are 6 independent switches which can be set off or on.
Garage Door OpenerKevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with six independent switches, each one set on or off. The receiver (wired to the door) must he set with the same pattern as the transmitter. (Exercises 71-74 are based on ideas similar to those of the “birthday problem” in theFor Further Thoughtfeature in this section.)
If five 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? (Give your answer to four decimal places.)
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