Question: The chance that any one telephone line is busy at a given moment of time is 0.01. What is the chance that out of 5 telephone lines, less than 3 lines are busy?
A ) 0.048 B ) .001 C ) 1 D ) 0.951
Steps to derive
1 The number of telephone lines is 5, n = 5.
2 A line being busy represents a success, x < 3 or x = 0, 1, 2.
3 The probability of a success, p = 0.01
4 The probability of failure, q = 1 - 0.01 = 0.99
5 P (0 lines are busy) = 5C0 (0.01)0(0.99)5 = (1) (1) (0.951) = 0.951.
6 P (1 line is busy) = 5C1 (0.01)1 (0.99)4 = (5) (0.01) (0.9606) = 0.048
7 P (2 lines are busy) = 5C2 (0.01)2 (0.99)3 = (10) (0.0001) (0.9703) = 0.001
8 P (less than 3 lines are busy) = P (0 lines are busy) + P (1 line is busy) + P (2 lines are busy) = 0.951 + 0.048 + 0.001. ≈ 1
