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Of 12 possible building sites for factories, 5 have buried toxic waste sites that no one told you about! If you choose 3 of the sites for initial building locations, what is the probability you will be lucky enough to avoid any toxic waste sites?

Respuesta :

Answer:

[tex]\frac{7}{44}[/tex]

Explanation:

Probability refers to the chance of occurrence of some event.

Number of building sites for factories = 12

Number of toxic waste sites = 5

So, number of non-toxic waste sites = 12 - 5 = 7

We need to find the probability that the 3 sites chosen for initial building locations are non-toxic.

Solution:

Probability = number of non-toxic waste sites / Number of building sites for factories = [tex]\frac{7_{C_{3}}}{12_C_{3}}=\frac{\frac{7!}{3!4!}}{\frac{12!}{3!9!}}=\frac{7\times 6\times 5}{3\times2}\times\frac{3\times2}{12\times11\times10}=\frac{7}{44}[/tex]

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