Question

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 ).

Answer 1

Answer:

$P(E^c)=\dfrac{1}{3}$

Step-by-step explanation:

The sample space for the experiment  is:

$S=\{9,10,11,12,13,14,15,16,17,18,19,20\}$

• Number of elements in S, n(S)=12

Given an event E such that:

$E=\{10,11,12,13,14,15,16,17\}$

• 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.

$E^c=\{9,18,19,20\}$

• Number of elements in the complement of E, $n(E^c)=4$

Therefore:

$P(E^c)=\dfrac{n(E^c)}{n(S)}\\ =\dfrac{4}{12}\\P(E^c)=\dfrac{1}{3}$