Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with five independent switches, each one on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter. If one of Kevin's neighbors also has this same brand of opener, and both of them set the switches randomly, what is the probability that they will use the same setting?

Question

Mathematics

Maribel Melton

5 March, 08:57

Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with five independent switches, each one on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter. If one of Kevin's neighbors also has this same brand of opener, and both of them set the switches randomly, what is the probability that they will use the same setting?

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Answers (1)

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Case Torres · Answer 1

0.03125

Step-by-step explanation:

Number of Combinations possible with the Transmitters = 2*2*2*2*2 = 32

Probability that they will use the same settings = 1 - Probability of them using different settings.

= 1 - 32*31 / (32^2)

=1 - 992/1024

= 1 - 0.96875

= 0.03125