Question 1132195
<br>
P(heads) = 1/2
P(tails) = 1/2
P(5 or 6) = 9/36 = 1/4
P(neither 5 nor 6) = 3/4<br>
P(heads before 5 or 6) =
P((heads on first flip) OR
 (tails on first flip AND neither 5 nor 6 on first roll AND heads on second flip) OR
 (tails on first flip AND neither 5 nor 6 on first roll AND tails on second flip AND neither 5 nor 6 on second roll AND heads on third flip) OR
...)<br>
= (1/2) + (1/2)(3/4)(1/2) + (1/2)(3/4)(1/2)(3/4)(1/2) + ...<br>
This is an infinite geometric series with first term 1/2 and common ratio (1/2)(3/4) = 3/8.<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....