SOLUTION: Matt flipped two fairs coins together. He continued doing so until at least one of the coins turns up heads. What is the probability that both are heads on the last flip? please ex

Algebra.Com
Question 583695: Matt flipped two fairs coins together. He continued doing so until at least one of the coins turns up heads. What is the probability that both are heads on the last flip? please explain
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Matt flipped two fairs coins together. He continued doing so until at least one of the coins turns up heads. What is the probability that both are heads on the last flip? please explain 
This could theoretically go on forever and Matt never get anything but tails.
So it is a infinite geometric series of probabilities.

He will always either get HH, HT, TH, or TT, each with probability of .

To succeed, Matt must get HH on the first throw or get only TT successively
a bunch of times and then HH on the final throw. 

So we want the probability of:

1. HH 1st time with probability 
OR
2. TT 1st time and HH 2nd time with probability  · = 
OR
3. TT 1st 2 times and HH 3rd time with probability · = 
OR
4. TT 1st 3 times and HH 4th time with probability · = 
OR
...

OR means "add", so the desired probability is the sum of this infinite
geometric series:

 +  +  +  + ...

the formula for which is

 =  where  = r = 

 =  =  =  =  = 

Edwin
RELATED QUESTIONS

Matt flipped two fair coins together. He continued doing so until at least one of the... (answered by sudhanshu_kmr)
Four coins are flipped. What is the probability two are heads, given at least one is... (answered by Fombitz)
Two coins are tossed. Find the probability that both coins turn up heads given that at... (answered by Alan3354)
The probability of flipping 2 coins and having at least one land heads up... (answered by stanbon)
Three coins are tossed.what is the probability of getting(a)all heads,(b)two heads,(c)at... (answered by natolino_2017)
8 coins are simultaneously flipped. What is the probability that heads are showing on at... (answered by robertb)
Four fair coins are flipped. What is the probability of getting three or more... (answered by richard1234)
Tom has three coins. Two are fair and one is an unfair coin weighted so that heads is... (answered by Edwin McCravy)
Tom has three coins. Two are fair and one is an unfair coin weighted so that heads is... (answered by Boreal)