SOLUTION: A man alternatively tosses a coin and throws a die beginning with a coin. The probability that he gets a head a coin before he gets 5 or 6 in the fir is1

Question 1132195: A man alternatively tosses a coin and throws a die beginning with a coin. The probability that he gets a head a coin before he gets 5 or 6 in the fir is1
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

P(heads) = 1/2
P(tails) = 1/2
P(5 or 6) = 9/36 = 1/4
P(neither 5 nor 6) = 3/4

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
...)

= (1/2) + (1/2)(3/4)(1/2) + (1/2)(3/4)(1/2)(3/4)(1/2) + ...

This is an infinite geometric series with first term 1/2 and common ratio (1/2)(3/4) = 3/8.

The formula for the sum of an infinite geometric series with first term a and common ratio r (|r|<1) is

You can do the calculation....
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