# Thread: Dice probability question... should be quick for you guys :)

1. ## Dice probability question... should be quick for you guys :)

I realized after I posted the title, this would be much easier with coins. Sorry.

Here is my question:

If you had to flip heads to win and you could re-flip ONCE, if you didn't flip heads on the first attempt, what is the probability of flipping heads?

Is it still 50/50 because the flip events are independent? Or is the probability higher of flipping heads if you can re-flip the first loss?

Thank you.

2. Originally Posted by Jaystats
Here is my question:
If you had to flip heads to win and you could re-flip ONCE, if you didn't flip heads on the first attempt, what is the probability of flipping heads
The answer is $\displaystyle \dfrac{3}{4}$.
The only way to not to win is to flip two tails.

3. Wouldn't that be 2/3 then?

Event 1. Flip heads - win
Event 3 Flip tails, flip heads - Win
Event 4 Flip tails flip tails lose.

4. Originally Posted by Jaystats
Wouldn't that be 2/3 then?
Event 1. Flip heads - win
Event 3 Flip tails, flip heads - Win
Event 4 Flip tails flip tails lose.
Nope.
$\displaystyle P(H\cup TH)=P(H)+P(TH)=\frac{1}{2}+\frac{1}{2}\frac{1}{2}= \frac{3}{4}$

5. Thanks.