An office has four phone lines. Each is busy about 10% of the time. Assume that the phone lines act independently. 1) What is the probability that all four phones are busy 2) What is the probability that atleast two of them are busy?
Answers
Given : An office has four phone lines. Each is busy about 10% of the time. Assume that the phone lines act independently.
To Find :
The probability that all four phones are busy
The probability that atleast two of them are busy
Solution:
Each is busy about 10% of the time.
p = 0.1
q = 1 - p = 0.9
n = 4
P(x) = ⁿCₓpˣqⁿ⁻ˣ
The probability that all four phones are busy
P(4) = ⁴C₄(0.1)⁴(0.9)⁰
= 0.0001
The probability that atleast two of them are busy
x = 2 , x = 3 , x = 4
= P(2) + P(3) + P(4)
= ⁴C₂(0.1)²(0.9)² + ⁴C₃(0.1)³(0.9)¹ + ⁴C₄(0.1)⁴(0.9)⁰
= 0.0486 + 0.0036 + 0.0001
= 0.0523
or
1 - P(0) - P(1)
= 1 - ⁴C₀(0.1)⁰(0.9)⁴ - ⁴C₁(0.1)¹(0.9)³
= 1 - 0.6561 - 0.2916
= 0.0523
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