Probability of the first coin toss being a head?

Question

You have 3 coins tossed independently.
If your first coin toss is a head, you get one dollar.

Q) What is the probability you get one dollar, given that you get 3 heads?
*The word given shouldn't be used, rather we're interested in the joint probability. Does the word given matter?

The answer is 1/8

I don't understand why, wouldn't it be 1, since if you have 3 coins and 3 heads, the first coin MUST be a head?

? · Accepted Answer

I agree that something is garbled in the statement of the problem.

P (the first coin is heads | all coins are heads)
would indeed be equal to 1.

Also, the probability that the first coin toss is heads ought to be 1/2, if the coins are fair.

So let me make a guess here: 
If the question was actually asking the probability that BOTH these events occur:
A = You get one dollar;
B = You get 3 heads;
then the joint probability of the two events, P(A and B), is indeed 1/8.

Probability of the first coin toss being a head?

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