Suppose you decided to keep flipping a coin until a tails came up, at which point you would stop. What is the probability of a tails coming up on the 6th flip of the coin?

Question

Suppose you decided to keep flipping a coin until a tails came up, at which point you would stop. What is  the probability of a tails coming up on the 6th flip of the coin?

jtvatsim · Answer

Have you tried anything so far? Where are you stuck? :)

hockeychick23 · Answer

well i thought i would just have  to divide 100 by 6 because theres an equal chance of getting the tails to come up on each and with that i got 16.7% but that doesn't seem right

jtvatsim · Answer

Hmm... OK. Let's solve an easier problem first. What is the probability of tails coming up on the first flip? Would you be able to solve that question?

hockeychick23 · Answer

yea theres a 50% chance

jtvatsim · Answer

Great! Now, let's make it a bit harder. This time I want to get tails on the second flip, but not on the first.

jtvatsim · Answer

To get tails on the second flip, but not the first, we must get this sequence:

1st    2nd
H        T

jtvatsim · Answer

Now, would you agree that the chances of getting H on the first flip is 50% or 0.5?

hockeychick23 · Answer

ohh i think i get it, i think its 1.6 because i have to divide by 2 6 times
the second time it would be 25%
3rd 12.5%
4th, 6.25%
5th, 3.125%
6th, 1.5625%

jtvatsim · Answer

That is the idea!

hockeychick23 · Answer

thanks!

jtvatsim · Answer

no problem, you solved it yourself! :)