Probability of requiring repair by the four cars in the first six months is equal to 0.009235.
As given in the question,
Probability of having repair requirement in the first six months = 31%
Success rate 'p' = 31%
= 0.31
1 - p = 1 - 0.31
= 0.69
Total number of cars 'n' = 4
Number of cars need to repair 'x' = 4
Probability for all the four cars require repairment in the first six months
= ⁿCₓ pˣ ( 1 - p)ⁿ⁻ˣ
= ⁴C₄ ( 0.31)⁴ ( 0.69)⁴⁻⁴
=( 4!/ (4-4)!4!) × ( 0.31)⁴ × 1
= ( 0.31)⁴
= 0.009235
Therefore, the probability of all the four cars require repairing in the first six months is equal to 0.009235.
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