Question

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?

Answer 1

0.03125

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