## probability

For students of class 11-12 (age 16+)
aroup
Posts: 7
Joined: Wed Dec 08, 2010 8:09 pm

### probability

a fair coin is tossed until a head appears or it has been tossed 4 times.given that a head does not appear in first 2 tosses.Find the probability that a coin was tossed 4 times?

solution: let H and T the head and tail.the sample space therefore
/* Q={H,TH,TTH,TTTH,TTTT} */

since the coin is fair,P[T]=P
Last edited by aroup on Sat Jan 15, 2011 7:59 pm, edited 2 times in total.
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abir91
Posts: 52
Joined: Sun Dec 19, 2010 11:48 am

### Re: probability

1) Because you are told to count until head appears or, you have tossed 4 times.

2) I don't see TTT in your sample space.

By the way, there is another (easier?) way to understand this. Since it is given that the outcome of the first two toss are tails, let's consider the third toss. It can be head , in that case we are done tossing. Or, it can be tail, in that case, we are also done tossing as we will stop on the fourth toss. So the chance is 1/2. Similarly, for the second question, the answer is 3/4. The following picture illustrates this:
Attachments
Red dots indicate desired sample points
coin.png (22.36 KiB) Viewed 2554 times
Abir

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aroup
Posts: 7
Joined: Wed Dec 08, 2010 8:09 pm

### Re: probability

thanks,now its clear
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geeknick
Posts: 4
Joined: Sat Nov 05, 2011 6:39 pm

### Re: probability

Is there any probability solver available online ????

nafistiham
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### Re: probability

$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
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