Question 1197528: An experiment consists of tossing 5 fair (not weighted) coins, except one of the coins has 5 a head on both sides. Compute the probability of obtaining exactly 2 heads.
Found 3 solutions by ikleyn, math_tutor2020, greenestamps:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
When I read your post, I can not get, what does it mean
" one of the coins has 5 a head on both sides ".
I am perplexed. Could you clarify, please.
Or, if you find it is an error, then edit your post and re-submit it to the forum.
In this case please do not submit it to me personally.
Also, could you explain it in clear way, what we really have:
- 5 normal fair coins and #6 special, OR this special is among 5 coins;
but then these 5 coins can not be called as " fair " coins.
As to me, it would be much better, if you will  it clearly  ,
what is given and what you want to obtain.
This forum is for Math; it is not for -bla - bla - bla- -bla - bla - bla- . . . . . . . . . . . . . . .
Answer by math_tutor2020(3817)  (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Ignoring one extra stray character "5" in the statement of the problem, it seems clear that the experiment involves tossing 5 fair coins, one of which has heads on both sides.
So that coin will definitely come up heads. So to find the probability that the result is exactly 2 heads, we need only find the probability that exactly 1 of the other 4 coins comes up heads. Since all the coins are fair, that is an easy calculation.
The probability of either heads or tails on each of the 4 coins is 1/2; and we need to choose 1 of the 4 coins to be the one that comes up heads:
P(exactly 2 heads) = 
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