Respuesta :
Answer:
The probability that 2 of those tested have defective brakes is 0.4196
Step-by-step explanation:
Consider the provided information.
Keith’s Florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 15 trucks, 6 have brake problems. A sample of five trucks is randomly selected.
Thus, total number of trucks N=15,
Number of trucks having brake problem (S) = 6
Number of sample trucks are n=5
[tex]P(X=x)=\frac{\binom{S}{x}\binom{N-S}{n-x}}{\binom{N}{n}}[/tex]
Substitute the respective values in the above formula.
[tex]P(X=2)=\frac{\binom{6}{2}\binom{15-6}{5-2}}{\binom{15}{5}}[/tex]
[tex]P(X=2)=\frac{\binom{6}{2}\binom{9}{3}}{\binom{15}{5}}[/tex]
[tex]P(X=2)=\frac{15\times 84}{3003}[/tex]
[tex]P(X=2)=\frac{15\times 84}{3003}[/tex]
[tex]P(X=2)\approx0.4196[/tex]
Hence, the probability that 2 of those tested have defective brakes is 0.4196
