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# Probability of getting 2 heads and 4 tails when flipping a coin 6 time

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4291

Kudos [?]: 7773 [0], given: 95

Probability of getting 2 heads and 4 tails when flipping a coin 6 time [#permalink]

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08 Mar 2017, 17:40
hernandezlarry1234 wrote:
Probability of getting 2 heads and 4 tails when flipping a coin 6 times

hernandezlarry1234,

I'm happy to help.

I saw your post without an answer so far, so I thought I would help.

Think about it this way. In the six flips, how many ways can we place the two heads? We need a combination for this.
See:
GMAT Permutations and Combinations
GMAT Math: Calculating Combinations

Here, the number of ways is 6C2 = 15. There are 15 cases.

In each case, we have six flips, and each one is either H or T. Both have a probability of 1/2, so any one case would have a probability of
$$\frac{1}{2^6} = \frac{1}{64}$$

Since there are 15 cases with identical probabilities, the total probability is
$$\frac{15}{2^6} = \frac{15}{64}$$

This particular setup is known as the Binomial situation in Probability. Here's a free lesson about it:
Binomial Situation

Does all this make sense?
Mike
_________________

Mike McGarry
Magoosh Test Prep

Kudos [?]: 7773 [0], given: 95

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Probability of getting 2 heads and 4 tails when flipping a coin 6 time   [#permalink] 08 Mar 2017, 17:40
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# Probability of getting 2 heads and 4 tails when flipping a coin 6 time

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