Thread: coin toss

Pete and Alex were tossing a penny against the restroom wall. If 3 heads are obtained before 3 tails, Pete wins, and if 3 tails come up first, Jimmy wins. After 3 tosses the results are HTH. The principle walks in at that moment and tells the boys to get on to class. What was the probability that Bobby would have won the game if they had been able to continue?

Originally Posted by ihavvaquestion

Pete and Alex were tossing a penny against the restroom wall. If 3 heads are obtained before 3 tails, Pete wins, and if 3 tails come up first, Jimmy wins. After 3 tosses the results are HTH. The principle walks in at that moment and tells the boys to get on to class. What was the probability that Bobby would have won the game if they had been able to continue?

Who is Bobby? Where did he come from?

Originally Posted by ihavvaquestion

Pete and Alex were tossing a penny against the restroom wall. If 3 heads are obtained before 3 tails, Pete wins, and if 3 tails come up first, Jimmy wins. After 3 tosses the results are HTH. The principle walks in at that moment and tells the boys to get on to class. What was the probability that Bobby would have won the game if they had been able to continue?

and Jimmy?

he wins 3/4, he only loses if it goes tails then tails and prob of that is 1/2 x 1/2

or easier to get it in your head think of it as, H heads, T tails, If it is H he wins, if it is TH he wins, if it is HT he wins, if it is TT he loses, and those are the only possible events that can occur

Pete is Jimmy and Alex is Bobby...sorry

Sorry here is how the ? should read

Pete and Alex were tossing a penny against the restroom wall. If 3 heads are obtained before 3 tails, Pete wins, and if 3 tails come up first, Alex wins. After 3 tosses the results are HTH. The principle walks in at that moment and tells the boys to get on to class. What was the probability that Pete would have won the game if they had been able to continue?

Originally Posted by ihavvaquestion

Sorry here is how the ? should read

Pete and Alex were tossing a penny against the restroom wall. If 3 heads are obtained before 3 tails, Pete wins, and if 3 tails come up first, Alex wins. After 3 tosses the results are HTH. The principle walks in at that moment and tells the boys to get on to class. What was the probability that Pete would have won the game if they had been able to continue?

If The next toss is H, Pete wins.
The probability of that is 0.5.

If the next is T followed immediately by H, again Pete wins.
The probability of that is 0.5(0.5)=0.25.

Otherwise TT and Pete loses, of which the probability is 0.25.

P(Pete wins)=0.5+0.25

This is a cleverly disguised ‘problem of points’,.
It goes back to the twelfth century at least.
Solved in the seventeenth century in correspondence between Pascal and Fermat.
It is very instructive to study their two very different approaches to the solution.