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g A probability experiment is conducted in which the sample space of the experiment is Upper S equals StartSet 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 comma 19 comma 20 EndSet . Let event Upper E equals StartSet 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 EndSet . Assume each outcome is equally likely. List the outcomes in Upper E Superscript c . Find Upper P (Upper E Superscript c ).

Respuesta :

Answer:

[tex]P(E^c)=\dfrac{1}{3}[/tex]

Step-by-step explanation:

The sample space for the experiment  is:

[tex]S=\{9,10,11,12,13,14,15,16,17,18,19,20\}[/tex]

  • Number of elements in S, n(S)=12

Given an event E such that:

[tex]E=\{10,11,12,13,14,15,16,17\}[/tex]

  • Number of elements in E, n(E)=8

The outcomes in the complement of E are the outcomes in S that are not in E.

[tex]E^c=\{9,18,19,20\}[/tex]

  • Number of elements in the complement of E, [tex]n(E^c)=4[/tex]

Therefore:

[tex]P(E^c)=\dfrac{n(E^c)}{n(S)}\\ =\dfrac{4}{12}\\P(E^c)=\dfrac{1}{3}[/tex]

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