<p>Blue Book Pg. 408 # 5</p>
<p>(Diagram shows a spinner with 6 sections labeled 1-6)
On the disk shown above, a player spins the arrow twice. The fraction a/b is formed, where a is the number of the sector where the arrow stops after the first spin and b is the number of the sector where the arrow stops after the second spin. On every spin, each of the numbered sectors has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction a/b is greater than 1?</p>
<p>The answer is 15/36.</p>
<p>I've already searched the forum but couldn't find an explanation that I fully understood. To solve the problem I tried (1/6 * 5/6) + (1/6 * 4/6) + .... + (1/6 * 1/6) / 36, but obviously I was way off. Please help</p>
<p>You have a spinner with 1,2,3,4,5,6 on it, right? If your first spin lands on 1, there is no way you can end up with a fraction 1/b > 1. Therefore, there are 0 fractions >1 in that case.</p>
<p>If you get 2/b, you have 1 possibilities of getting a value >1, and that is 2/1.</p>
<p>If you get 3/b, you have 2 possibilities of getting a value >1, and those are 3/1 and 3/2.</p>
<p>If you get 4/b, you get 3 possibilities and so on, all the way up to 6.</p>
<p>You end up getting (1+2+3+4+5)/36. The denominator is 36 because there are 6*6 possible fractions.</p>
<p>Alpha2018:
You weren't all that far off, you just don't need that last division by 36.</p>
<p>(1/6 * 5/6) + (1/6 * 4/6) + .... + (1/6 * 1/6) = (5+4+3+2+1)/36 = 15/36</p>
<p>Seems likes this is under control but, just in case, here you are:</p>
<p>You know that A HAS to be greater than B, right? A/B > 1 so that means A MUST be greater than B.
So if A lands on 6, you can have 6/5, 6/4, 6/3, 6/2, 6/1. Boom, that's 5.
If A lands on 5, you can have 5/4, 5/3, 5/2, 5/1. Boom, that's 4.
If A lands on 4, you can have 4/3, 4/2,4/1. Boom, that's 3.
If A lands on 3, you can have 3/2, 3/1. Boom, that's 2.
If A lands on 2, you can have 2/1. Boom, that's 1.
Add 5+4+3+2+1 up, and you have 15.</p>
<p>Since there were 6 outcomes by 6 outcomes, 6 by 6 is 36. Thus, 15/36.</p>