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Probability-A fair coin is flipped 5 times

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Probability-A fair coin is flipped 5 times [#permalink] New post 10 Aug 2015, 12:07
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38% (00:23) correct 61% (00:26) wrong based on 21 sessions
Does anyone has a faster way of solving this problem instead of drawing out the tree?

A fair coin is flipped 5 times.

Quantity A: The probability of getting more heads than tails
Quantity B: 1/2
[Reveal] Spoiler: OA
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Re: Probability [#permalink] New post 11 Aug 2015, 22:13
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goneewindy wrote:
Does anyone has a faster way of solving this problem instead of drawing out the tree?

A fair coin is flipped 5 times.

Quantity A: The probability of getting more heads than tails
Quantity B: 1/2



There are 32 sample solutions in the solution set of the 5 coin toss. Since \(2^5 = 35\)
Now there are 5 coins so number of Heads can either be greater than or less than Tails. Since each head or tail is equally likely the probability of getting more heads is 0.5 or 16/32. The sample space is divided in two groups, "heads are more" and "tails are more".

If there had been even number of coins say 6. The sample space would have been 64. Now it wold have been divided into 3 groups, "heads are more" "tails are more" and "heads are equal to tails".
Now the "equal" case has 20 solutions. \(6!/3!*3!\) =20. The remaining 44 sample space points are equally likely to have heads or tails more.


Don't use logic unless you are well versed with probability theory. It is always easier and safer to draw the tree if you have the time.
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Re: Probability [#permalink] New post 12 Aug 2015, 01:39
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Solution


One solution can be simple manual combination techniques. As already discussed there can be \(2^5\) or 32 possible outcomes. The following cases are the relevant ones where the number of heads is more than tails:
  • 3 Heads 2 Tails: Total number of occurences is \((5!)/(3!)(2!)\) = 10
  • 4 Heads 1 Tail : Total number of occurences is \((5!)/(4!)(1!)\) = 5
  • 5 head 0 Tail : Total number of occurences is \((5!)/(5!)\) = 1

If you add the above occurrences it adds upto 16. So the probability is 16/32 or 1/2.
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Re: Probability [#permalink] New post 07 Jul 2017, 08:08
soumya1989 wrote:

Solution


One solution can be simple manual combination techniques. As already discussed there can be \(2^5\) or 32 possible outcomes. The following cases are the relevant ones where the number of heads is more than tails:
  • 3 Heads 2 Tails: Total number of occurences is \((5!)/(3!)(2!)\) = 10
  • 4 Heads 1 Tail : Total number of occurences is \((5!)/(4!)(1!)\) = 5
  • 5 head 0 Tail : Total number of occurences is \((5!)/(5!)\) = 1

If you add the above occurrences it adds upto 16. So the probability is 16/32 or 1/2.



Plz clarify does it have the same meaning if the ques ask-

Probability of getting more heads than tails or the probability of getting at least 3 heads??
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Re: Probability [#permalink] New post 07 Jul 2017, 11:06
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pranab01 wrote:

Plz clarify does it have the same meaning if the ques ask-

Probability of getting more heads than tails or the probability of getting at least 3 heads??


Yes it is!
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Re: Probability-A fair coin is flipped 5 times [#permalink] New post 07 Apr 2018, 08:16
Probability of getting 3 heads = 1/2 * 1/2 * 1/2 *1 * 1 = 1/8
Probability of getting 4 heads = 1/2 * 1/2 * 1/2 *1/2 * 1 = 1/16
Probability of getting 5 heads = 1/2 * 1/2 * 1/2 *1/2 * 1/2 = 1/32

The probability of getting 3 or 4 or 5 heads = 1/8+1/16+1/32 = 7/32
Re: Probability-A fair coin is flipped 5 times   [#permalink] 07 Apr 2018, 08:16
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