The probability that if 5 tires are inspected, exactly 1 has a defect is 0.204
The probability that a tire is defect is given as:
p = 5%
The required probability is then calculated using:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x}[/tex]
Where:
n = 5 --- number of tires
x = 1 ---number of tires with defect
So, we have:'
[tex]P(1) = ^5C_1 * (5\%)^1 * (1 - 5\%)^{5 - 1}[/tex]
This gives
[tex]P(1) = 5 * (5\%) * (1 - 5\%)^4[/tex]
Evaluate the product
P(1) = 0.204
Hence, the probability that if 5 tires are inspected, exactly 1 has a defect is 0.204
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