# Thread: When is a fair coin toss not fair?

1. ## When is a fair coin toss not fair?

Here's a real twister. I'm not sure if I'm overthinking it?

A fair coin is tossed 6 independent times with the result of 4 heads and 2 tails. What was the most likely number of heads after the first 4 tosses?

Now, I'm not sure if this is a trick question, and the right answer is just 2, or if I need to take into consideration that the probability of a heads in these first 6 tosses is 4 out of 6 - or is it still 1 out of two?

2. Originally Posted by ScienceGeniusGirl
Here's a real twister. I'm not sure if I'm overthinking it?

A fair coin is tossed 6 independent times with the result of 4 heads and 2 tails. What was the most likely number of heads after the first 4 tosses?

Now, I'm not sure if this is a trick question, and the right answer is just 2, or if I need to take into consideration that the probability of a heads in these first 6 tosses is 4 out of 6 - or is it still 1 out of two?
You are told apriori that the coin is fair.

You are being asked to find the number N of heads in the first four throws that has maximum probability, given that there are 4 head in the first 6 tosses.

CB

3. How would I go about that?

4. Originally Posted by ScienceGeniusGirl
How would I go about that?
One way:

List all sequences of 6 tosses with 4 heads and 2 tails.

there are 15.

Of these 6 have 2 heads in the first 4 tosses, 8 have 3 heads in the first 4 tosses, and 1 has all heads in the first 4 tosses.

CB