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# If a certain coin is flipped, it has probability ½ of landing on heads

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42
GPA: 3.82
If a certain coin is flipped, it has probability ½ of landing on heads  [#permalink]

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26 Dec 2018, 01:47
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5% (low)

Question Stats:

83% (00:59) correct 17% (01:33) wrong based on 63 sessions

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[Math Revolution GMAT math practice question]

If a certain coin is flipped, it has probability $$\frac{1}{2}$$ of landing on heads and probability $$\frac{1}{2}$$ of landing on tails. If the coin is flipped $$4$$ times, what is the probability that it will land on tails at least once?

$$A. \frac{3}{8}$$
$$B. \frac{1}{4}$$
$$C. \frac{1}{2}$$
$$D. \frac{5}{16}$$
$$E. \frac{15}{16}$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend Joined: 18 Aug 2017 Posts: 4252 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: If a certain coin is flipped, it has probability ½ of landing on heads [#permalink] ### Show Tags 26 Dec 2018, 02:24 MathRevolution wrote: [Math Revolution GMAT math practice question] If a certain coin is flipped, it has probability $$\frac{1}{2}$$ of landing on heads and probability $$\frac{1}{2}$$ of landing on tails. If the coin is flipped $$4$$ times, what is the probability that it will land on tails at least once? $$A. \frac{3}{8}$$ $$B. \frac{1}{4}$$ $$C. \frac{1}{2}$$ $$D. \frac{5}{16}$$ $$E. \frac{15}{16}$$ P ( of only heads) = 1/2 and 4 times would be (1/2)^4 = 1/16 P of at least one tails 1-1/16 = 15/16 IMO E _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Intern Joined: 03 Nov 2018 Posts: 3 Re: If a certain coin is flipped, it has probability ½ of landing on heads [#permalink] ### Show Tags 26 Dec 2018, 03:20 Probability of atleast one formula = 1- Probability of opposite event In this case Probability of only head = 1/2 Probability of only head when coin is flipped 4 times = (1/2)^4 = 1/16 Probabilty of atleast one tails = 1- 1/16 = 15/16 e-GMAT Representative Joined: 04 Jan 2015 Posts: 2943 Re: If a certain coin is flipped, it has probability ½ of landing on heads [#permalink] ### Show Tags 26 Dec 2018, 09:06 3 Solution Given: When a coin is tossed, • Probability of head = $$\frac{1}{2}$$ • Probability of tail = $$\frac{1}{2}$$ To find: • The probability of getting at least one tail, if the coin is tossed 4 times Approach and Working: Method 1: P (at least 1 tail) = P (1 tail AND 3 heads) OR P (2 tails AND 2 heads) OR P (3 tails AND 1 head) OR P (4 tails) = $$\frac{1}{2}^4 * \frac{4!}{3!}$$ + $$\frac{1}{2}^4 * \frac{4!}{2!2!}$$ + $$\frac{1}{2}^4 * \frac{4!}{3!}$$ + $$\frac{1}{2}^4$$ = $$\frac{15}{16}$$ Method 2: P (at least 1 tail) = 1 – P (all heads) = 1 – $$\frac{1}{2}^4$$ = 1 – $$\frac{1}{16}$$ = $$\frac{15}{16}$$ Hence, the correct answer is option E. Answer: E _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7612 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If a certain coin is flipped, it has probability ½ of landing on heads [#permalink] ### Show Tags 28 Dec 2018, 03:19 => The complementary case is the event with all heads, which has probability $$(\frac{1}{2})^4$$. The probability of at least one tail is $$1 – (\frac{1}{2})^4 = 1 – \frac{1}{16} = \frac{15}{16}.$$ Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If a certain coin is flipped, it has probability ½ of landing on heads   [#permalink] 28 Dec 2018, 03:19
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