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

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

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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. $$\frac{3}{8}$$
[Reveal] Spoiler: OA

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

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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) $$= \frac{6}{16} = \frac{3}{8}$$

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

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04 Aug 2017, 04:41
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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. $$\frac{3}{8}$$

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

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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.

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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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