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# Aptitude - Probability - Discussion

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"The secret to creativity is knowing how to hide your sources."
- Albert Einstein
5.

Three unbiased coins are tossed. What is the probability of getting at most two heads?

[A].
 3 4
[B].
 1 4
[C].
 3 8
[D].
 7 8

Explanation:

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

Let E = event of getting at most two heads.

Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.

 P(E) = n(E) = 7 . n(S) 8

 Sundar said: (Fri, Aug 20, 2010 01:01:14 AM) Hi Guys, At most two heads means "Total number of HEADs can be 0 to 2". So we cannot include HHH, because it contains 3 heads. But we can include TTT, because ZERO head is accepted. Therefore, the given answers is perfectively correct. You may ask your doubts here if you have regarding this question? Have a nice day!

 Malarvizhi said: (Sun, Oct 31, 2010 05:14:16 AM) How did say n(s) is 8?

 Sundar said: (Sat, Nov 20, 2010 08:41:01 AM) @Malarvizhi Note: "At most two heads" --(means)--> Not more than two heads. Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} <--- (8 combinations) Therefore, n(S) = 8.

 Abhijit said: (Fri, Dec 3, 2010 04:24:32 AM) Total no of probabilities= 2^3 =8 for 2/1/0 heads probability is =7(only 1 left HHH)

 Dharini said: (Sun, Dec 19, 2010 12:26:40 PM) I cant follow what abhijit said why it is 2 power 3?

 Murugesh said: (Sat, Jan 1, 2011 11:05:09 AM) @dharini... 2---> H & T 3---> total no of coins. so 2^3.

 Dinesh said: (Tue, Jan 4, 2011 08:07:40 AM) Got it murugesh thanks..

 Sathya said: (Thu, Mar 24, 2011 07:18:45 AM) What is unbiased coins?

 Sathish said: (Sat, Apr 30, 2011 07:04:48 AM) Thank you sundar.

 Sara said: (Mon, May 23, 2011 09:21:00 AM) Won't it be 3 out of 8?

 Puttz said: (Thu, Jun 9, 2011 02:58:23 PM) Unbiased coins means a coin having head and tail whereas a biased coin means having two heads or two tails respectively.

 Durgaprasad said: (Tue, Aug 9, 2011 11:18:56 AM) Thanks sundar. Superb explanation.

 Kruvy said: (Wed, Sep 28, 2011 03:31:09 PM) @Sundar , I like the way you explained. thanks mate.

 Swetha said: (Sat, Nov 5, 2011 11:39:27 AM) Very clear explanation sundar..Thank you!

 Uday said: (Sat, Nov 12, 2011 10:15:27 PM) How we can do with this ^ symbol ?

 Arpan said: (Sat, Dec 3, 2011 12:47:36 AM) Abhijeet that's not the way to do this prob. You got it totally wrong. But your answer is matching. Have a look at Sundar's answer.

 Saurabh Patel said: (Fri, Feb 10, 2012 08:34:40 PM) If the leatter of the word LUCKNOW are randomly arrenged, find the proabibility of always having the word NOW.

 Manju said: (Tue, Feb 28, 2012 02:32:19 PM) How many times a man can tossing a coin so that the probability of atleast one head is more than 80%?

 Sujit said: (Fri, Nov 16, 2012 08:18:17 PM) SOURAV If NOW will be together all the time all the time then take "NOW" as one letter. Lucknow will be considered as 5 letters. Then you can get the answer easily.

 Ravi said: (Tue, Dec 25, 2012 11:06:16 AM) You ask most two head but why you considered zero head?