Ask Question
4 October, 20:41

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 six 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?

+1
Answers (1)
  1. 4 October, 23:06
    0
    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 six neighbors with the same type of opener set their switches independently. The probability of at least one pair of neighbors using the same settings is 0.65633

    Step-by-step explanation:

    Step 1

    In the question it is given that

    Automatic garage door opener utilizes a transmitter control with four independent switches

    So. the number of Combinations possible with the Transmitters =

    2*2*2*2 = 16

    Step 2

    Probability of at least one pair of neighbors using the same settings = 1 - Probability of All Neighbors using different settings.

    = 1 - 16*15*14*13*12*11 / (16^6)

    Step 3

    Probability of at least one pair of neighbors using the same settings=

    = 1 - 0.343666

    Step 4

    So the probability of at least one pair of neighbors using the same settings

    is 0.65633
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers