Question

A person chooses 2 different numbers from a set of the integers from −5 to −1, inclusive. The result of the experiment is the sum of the two chosen numbers. Find the set representing the event E that the sum is less than −6. Give your answer as a set, e.g. {1,2,3}, and do not include E= in your answer.

Answer 1

Given a set of integers from -5 to -1

$\mleft\lbrace-5,-4,-3,-2,-1\mright\rbrace$

The experiment is "choose two numbers at random from the set and add them"

The possible combinations are:

$\begin{gathered} -1;-2\to(-1)+(-2)=-3 \\ -1;-3\to(-1)+(-3)=-4 \\ -1;-4\to(-1)+(-4)=-5 \\ -1;-5\to(-1)+(-5)=-6 \\ -2;-3\to(-2)+(-3)=-5 \\ -2;-4\to(-2)+(-4)=-6 \\ -2;-5\to(-2)+(-5)=-7 \\ -3;-4\to(-3)+(-4)=-7 \\ -3;-5\to(-3)+(-5)=-8 \\ -4;-5\to(-4)+(-5)=-9 \end{gathered}$

Event E is defined as "all sums whose results are less than -6"

As you can see, there are only 3 results of the possible combinations that are less than -6, those are:

$\mleft\lbrace-3,-4,-5\mright\rbrace$