Respuesta :
Given:
[tex]\begin{gathered} Total\text{ N}umber\text{ of sprockets = 37} \\ Number\text{ of defective sprockets = 4} \\ Number\text{ of non-defective sprockets = 33} \end{gathered}[/tex]Required:
The probability that all in the sample are defective.
The probability that none in the sample is defective.
Explanation:
(a) 5 sprockets are selected probability that all are defective favorable cases are 1 which means all 4 are defective.
The number of ways of selecting 4 from 4 defective sprockets is,
[tex]^4C_4[/tex]The required probability is calculated as,
[tex]\begin{gathered} Probability=\text{ }\frac{^4C_4}{^{37}C_4} \\ Probability=\text{ }\frac{1}{66045} \\ \end{gathered}[/tex]Thus the probability that all selected is 1/66045.
(b) The 4 sprockets selected are non-defective.
The number of ways of selecting 4 sprockets is,
[tex]^{33}C_4[/tex][tex]^4C_4[/tex]The required probability is calculated as,
[tex]\begin{gathered} Probability\text{ = }\frac{^{33}C_4}{^{37}C_4} \\ Probability\text{ = }\frac{40920}{66045} \\ Probability\text{ = 0.6196} \end{gathered}[/tex]Answer:
Thus the probability that all selected is 1/66045.
Thus the probability of selecting 4 non-defective sprockets is 0.6196.
