Event 'A' has a 50% chance of ocurring.

The only way event 'B' can occur is if event 'A' occurs;
If event 'A' occurs, event 'B' has a 50% chance of occuring.

The only way event 'C' can occur is if event 'B' occurs;
If event 'B' occurs, event 'C' has a 50% chance of occuring.

What are the chances of event 'C' occuring?

I think it is 50% x 50% x 50% = 12.5%, but I am not sure that is right.
Please show your math if I am wrong.

Let's say the action you're talking about is a flip of the coin, and
the "event" would be the coin coming up Heads.


For the first flip, you have a %100 chance of getting to flip, and 50%
chance it comes up heads.

There's then a 50% chance of a second flip, and a 50% chance of that
being Heads -- .50 * .50 = 25%.

So...there's a 25% chance of getting to a third flip, which has a
50/50 chance of Heads -- .25 * .50 = 12.5%

As you thought, the odds are 12.5%.


Cheers,,

pafalafa-ga

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Clarification of Answer by pafalafa-ga on 28 Dec 2006 10:22 PST

It dawned on me this might be some math homework for school, and that
you might like some extra help.  If so, just let me know by posting a
note, here, and I'll provide whatever math homework help I can. 
Probability is always a fascinating, but challenging topic.

Cheers,

Dave

P(A)=0.5
P(B/A)=0.5
P(C/A?B) = 0.5

Therefore,
P(C) = P(A?B?C) = P(A)* P(B/A)* P(C/A?B) = 0.5*0.5*0.5
P(C) = 0.125 = 12.5%