Question 1132192
<br>
P(5) = 4/36 = 1/9
P(7) = 6/36 = 1/6
P(neither 5 nor 7) = 26/36 = 13/18<br>
P(5 before 7) = 
P((5 on first flip) OR
 (neither 5 nor 7 on first flip AND 5 on second flip) OR
 (neither 5 nor 7 on first flip AND neither 5 nor 7 on second flip AND 5 on third flip) OR
...) = <br>
1/9 + (13/18)(1/9) + (13/18)(13/18)(1/9) + ...<br>
This is an infinite geometric series with first term a = 1/9 and common ratio r = 13/18.<br>
The formula for the sum of an infinite geometric series with first term a and common ratio r (|r|<1) is<br>
{{{S = a/(1-r)}}}<br>
You can do the calculation.