Very tricky.

Hi,
H on 3rd coin is fixed. But each of the other 9 coins can be either head or tail
So, number of outcomes is 1.(2)^9

Hence, B

Didn't get it.
What's the reason that it turns head 512 times??

Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

Start by calculating the number of distinct results possible when tossing ten coins:

Since every coin has 2 possible outcomes, the number of possible result combinations for all ten coins is 2^10 (2*2*2... ten times).


Next, narrow down the number of results to those in which the third coin shows 'heads':

Since the probability of receiving 'heads' on the third coin flip is 1/2, exactly half of the ten-coin result combinations include the third coin showing 'heads'. Therefore, divide the total number of results by 2:

2^10 / 2 = 2^10 / 2^1 = 2^(10-1) = 2^9.

The correct answer is B.

Answer is 2^9

Wonderful Roy,
So simple yet so difficult.

I wonder, why it didn't click me!

winniethepooh wrote:Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

2^10
2^9
3 * 2^8
3 * 2^9
None of these

Since the total number of outcomes of the 10 coins is 2^10, and half of these outcomes will have the third coin turning up as a head (the other half will have the third coin as a tail), we see that the number of outcomes with the third coin turning up as a head is ½ x 2^10 = 2^9.

Answer: A