<p>What is the probability that a diagonal randomly selected from a regular octagon connects opposite vertices? express your answer as a common fraction.</p>
<p>if someone could explain how to do this problem, it would be of much help.</p>
<p>answer = 1/5</p>
<p>Ford help me.</p>
<p>First I would recommend drawing a right octagon for this problem. Okay pick a point on the octagon. Then draw all possible diagonals; there are 5. There can only be one possible that is directly opposite (directly on the opposite side). So the probability is 1/5. </p>
<p>Hope this helps.</p>
<p>Yes, I was actually thinking about that earlier, but what about all the other side’s diagonals? Don’t you need to factor those in too? why or why not?</p>
<p>You don’t have to worry because the analysis etennis used at one diagonal would apply at any of them. </p>
<p>If you don’t believe that, then you can do the problem another way:</p>
<p>There are 8 vertices. To make a diagonal, you have two pick 1 of them.
Then there are 5 choices for the other vertex. 8 *5 = 40 but that would count each diagonal twice (AB and BA are the same segment) so 40/2= 20 possible diagonals.</p>
<p>Of the 20, only 4 are formed by opposite vertices. So 4/20 = 1/5. </p>
<p>But again, since there is nothing to distinguish one vertex from another, you really could have trusted the first method which is quicker.</p>
<p>First, figure out how many diagonals there are in an octagon. </p>
<p>There are:</p>
<p>5+5+4+3+2+1=20 (If you draw the picture, this is clear)</p>
<p>Now figure out how many have ‘opposite’ vertices.</p>
<p>Obviously just 4.</p>
<p>P=4/20=1/5</p>