# An experiment on the probability is carried out, in which the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let event

An experiment on the probability is carried out, in which the sample space of the experiment is
$S=1,2,3,4,5,6,7,8,9,10,11,12.$
Let event $E=2,3,4,5,6,7,event$
.
Assume that each outcome is equally likely. List the outcome s in For G.
Now find P( For G) by counting the number of outcomes in For G.
Determine P (For G ) using the General Addition Rule.

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Step 1

Step 2
The set above has 8 elements, there are 12 possible outcomes, therefore

Using the General Addition Rule gives:
$P\left(F\cup G\right)=P\left(F\right)+P\left(G\right)-P\left(F\cap G\right)$
$P\left(F\cup G\right)=\frac{5}{2}+\frac{4}{12}-P\left(E\cap H\right)$
$P\left(F\cup G\right)=\frac{6}{12}+\frac{3}{12}-\frac{1}{12}$
$P\left(F\cup G\right)=\frac{8}{12}-\frac{2}{3}$