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If you are flipping the coin 4 times, what is the probability of landi

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If you are flipping the coin 4 times, what is the probability of landi [#permalink]

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New post 04 Aug 2017, 02:26
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If you are flipping the coin 4 times, what is the probability of landing on head two times?

A. \(\frac{3}{5}\)
B. \(\frac{4}{5}\)
C. \(\frac{3}{7}\)
D. \(\frac{4}{7}\)
E. \(\frac{3}{8}\)

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Re: If you are flipping the coin 4 times, what is the probability of landi [#permalink]

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New post 04 Aug 2017, 03:07
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MathRevolution wrote:
If you are flipping the coin 4 times, what is the probability of landing on head two times?

A. \(\frac{3}{5}\)
B. \(\frac{4}{5}\)
C. \(\frac{3}{7}\)
D. \(\frac{4}{7}\)
E. \(\frac{3}{8}\)


Coin is tossed \(4\) times.

P (\(2\) heads) \(= (\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} )* 4C2\)

P (\(2\) heads) \(= (\frac{1}{16}) * (\frac{4!}{2!2!})\)

P (\(2\) heads) \(= (\frac{1}{16}) *(\frac{4 * 3 * 2!}{2 * 1 * 2!})\)

P (\(2\) heads) \(= \frac{6}{16} = \frac{3}{8}\)

Answer (E)...


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If you are flipping the coin 4 times, what is the probability of landi [#permalink]

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New post 04 Aug 2017, 04:41
1
MathRevolution wrote:
If you are flipping the coin 4 times, what is the probability of landing on head two times?

A. \(\frac{3}{5}\)
B. \(\frac{4}{5}\)
C. \(\frac{3}{7}\)
D. \(\frac{4}{7}\)
E. \(\frac{3}{8}\)



Two results for each of four coin flips. When ways to perform tasks in series, we multiply. So that is 2×2×2×2 results in total. That is 2[square]4 or 16.

For the favourable case we need to count the ways to get 2 heads and 2 tails. The count of permutations of two pairs of symbols is: 4!/2!2!=6. This is easily confirmed by just counting.


|HHTT,HTHT,HTTH,THHT,THTH,TTHH}=6
Thus the probability is: 6/16, or:
0.375
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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 5846
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Re: If you are flipping the coin 4 times, what is the probability of landi [#permalink]

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New post 06 Aug 2017, 18:18
==> Probability=Want/Total. Total=since the number of ways when throwing the coins each becomes head or tail 2 times, you get 2*2*2*2=16. Want=if it lands on head 2 times, it lands on tail 2 times, so you get 4!/2!2!=6. Thus, the probability=6/16=3/8.

The answer is E.
Answer: E
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Re: If you are flipping the coin 4 times, what is the probability of landi   [#permalink] 06 Aug 2017, 18:18
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