Answer:
11/16
Step-by-step explanation:
You could list all the possible fractions you will get:
Here are the's with 4 as the numerator:
4/4
4/5
4/6
4/7
Here are the one's with 5 as the numerator:
5/4
5/5
5/6
5/7
Here are the one's with 6 as the numerator:
6/4
6/5
6/6
6/7
Here are the one's with 7 as the numerator:
7/4
7/5
7/6
7/7
There are 4(4) different numerator-denominator combinations we can get.
Let's see which of these are bigger than 5/6.
If you think it is easier to look at the decimals of all these you can.
5/6=0.8333333333
----
4/4 =1
4/5 =0.8
4/6 =0.6666666666
4/7 =0.5714 (approximately)
There is only 1 bigger than 5/6 in this section.
5/4 =1.25
5/5 =1
5/6 =0.83333333333
5/7 =0.714 (approximately)
There is 2 bigger than 5/6 in this section.
6/4 =1.5
6/5 =1.2
6/6 =1
6/7 =0.857 (approximately)
There is 4 bigger than 5/6 in this section.
7/4
7/5
7/6
7/7
All of these are 1 or bigger because the numerator is bigger than or equal to the denominator so all 4 of these are bigger than 5/6 in this section.
P(fraction being greater than 5/6)=[\tex]\frac{\text{ the numbers I listed bigger than } \frac{5}{6}}{\text{ all the fractions I listed }}[/tex]
P(fraction being greater than 5/6)=[\tex]\frac{4+4+2+1}{4(4)}=\frac{11}{16}{/tex]
11/16
