A person has bought a table from an online furniture store. The seller delivers the disassembled table parts along with some screws to assemble it. The probability of a screw being defective is 1/12 . To compensate for the manufacturing error, the seller sends two extra screws in the package where the table needs exactly 10
screws to assemble. What is the probability that the buyer will be able to assemble the table?
Answers
Given : The probability of a screw being defective is 1/12
To compensate for the manufacturing error, the seller sends two extra screws in the package where the table needs exactly 10 screws to assemble.
To Find : the probability that the buyer will be able to assemble the table
Solution:
The probability of a screw being defective is 1/12
p = 1/12
q = 1 - p = 11/12
n = 12 ( 10 + 2 Extra )
buyer will be able to assemble the table
if atleast 10 screws are good
=> Defective screws are less than 3
defective screws are 0 , 1 or 2
P(x) = ⁿCₓpˣqⁿ⁻ˣ
probability that the buyer will be able to assemble the table
= P(0) + P(1) + P(2)
= ¹²C₀(1/12)⁰(11/12)¹² + ¹²C₁(1/12)¹(11/12)¹¹ + ¹²C₂(1/12)²(11/12)¹⁰
= ( 11¹² + 12*11¹¹ + 66*11¹⁰)/ 12¹²
= 0.92799
= 0.928
probability that the buyer will be able to assemble the table = 0.928
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