Mayco, a mail-order department store, has four telephone lines available for customers who wish to place their orders. If the probability that during business hours any one of the four telephone lines is engaged is , find the probability that when a customer calls to place an order all four lines will be in use.
A) 0.0007
B) 0.0384
C) 1
D) 0.0016

Question

Mayco, a mail-order department store, has four telephone lines available for customers who wish to place their orders. If the probability that during business hours any one of the four telephone lines is engaged is  , find the probability that when a customer calls to place an order all four lines will be in use.
A) 0.0007 
B) 0.0384 
C) 1 
D) 0.0016

Quizplus · Accepted Answer

The probability that any one of the four telephone lines is engaged is 11eab448_e7b9_7fa5_acdb_c9443a92694e_TB6027_11. 
Therefore, the probability that any one of the four telephone lines is free is 1 - 11eab448_e7b9_7fa5_acdb_c9443a92694e_TB6027_11.
When a customer calls to place an order, the probability that a line is free is independent of the probability that another line is free. 
Therefore, the probability that all four lines are in use is (11eab448_e7b9_7fa5_acdb_c9443a92694e_TB6027_11)^4 = 0.0016. 
Hence, the answer is D.

Mayco, a Mail-Order Department Store, Has Four Telephone Lines Available