SOLUTION: A fair coin is tossed until it comes up tails for the third time or heads for the second time. My set that I got was: HH TTT THTH HTH THTT HTTH HTTT THH TTHH TTHT What is the p

Algebra ->  Probability-and-statistics -> SOLUTION: A fair coin is tossed until it comes up tails for the third time or heads for the second time. My set that I got was: HH TTT THTH HTH THTT HTTH HTTT THH TTHH TTHT What is the p      Log On


   

Question 725450: A fair coin is tossed until it comes up tails for the third time or heads for the second time.
My set that I got was: HH TTT THTH HTH THTT HTTH HTTT THH TTHH TTHT
What is the probability that the third tail does occur?(Trick question)
What is the probability that the third tail doesn't occur?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First make a probability tree of all the possible outcomes (given the restriction rules)


The values in red are the probabilities for each scenario. For example, there’s a 12.5% chance of flipping THH (start at the top and go left, right, right)

Circle all the probabilities where T shows up 3 times to get this



Add up all those circled probabilities: 12.5+6.25+6.25+6.25 = 31.25

So the probability of that the third tail does occur is a 31.25% chance, which in decimal form is 0.3125