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If a coin has an equal probability of landing heads up or tails up eac

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Bunuel
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If a coin has an equal probability of landing heads up or tails up eac [#permalink] New post   11 Oct 2019, 04:24
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If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?

(A) 0.125
(B) 0.25
(C) 0.375
(D) 0.50
(E) 0.666
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C
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Re: If a coin has an equal probability of landing heads up or tails up eac [#permalink] New post   11 Oct 2019, 04:30
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Bunuel wrote:
If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?

(A) 0.125
(B) 0.25
(C) 0.375
(D) 0.50
(E) 0.666


total fair chances ; 1/2*1/2*1/2 = 1/8 ; .125
and getting heads twice in 3 flips we have
HHT; HTH; THH ; 3 ways so .125*3 ; .375
IMO C
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If a coin has an equal probability of landing heads up or tails up eac [#permalink] New post   11 Oct 2019, 04:37
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P(getting heads) = P(getting tails) = 0.5 (50%)

We have to determine the probability of getting exactly 2 Heads in three consecutive flips. Therefore, we have H, H and T. We have to see the possible cases.
1) HTH
2) HHT
3) THH

Thus, total test cases with exactly 2 H are: 3

Also, the total cases will be 8.
P(H=O) + P(H=1) + P(H=2) + P(H=3)
= 1 + 3 + 3 + 1
= 8

Thus, the required probability = 3/8= 0.375

(C)

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Re: If a coin has an equal probability of landing heads up or tails up eac [#permalink] New post   11 Oct 2019, 04:48
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3C2×(1/2)²×1/2=3/8=0.375
Option C

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Re: If a coin has an equal probability of landing heads up or tails up eac [#permalink] New post   12 Oct 2019, 04:12
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Archit3110 wrote:
Bunuel wrote:
If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?

(A) 0.125
(B) 0.25
(C) 0.375
(D) 0.50
(E) 0.666


total fair chances ; 1/2*1/2*1/2 = 1/8 ; .125
and getting heads twice in 3 flips we have
HHT; HTH; THH ; 3 ways so .125*3 ; .375
IMO C


Hello, thanks for the solution.

Kindly explain why we have to consider 3 different scenarios for the flips.

I assumed that one flip is when we get either a head or a tail and that we have adequately covered the 3 consecutive flips by 1/2*1/2*1/2 = 1/8

Why then are we considering 3 different flips when the question hasn't explicitly told us that 3 different events took place?

Thanks
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Re: If a coin has an equal probability of landing heads up or tails up eac [#permalink] New post   17 Mar 2020, 02:18
OmotayoH wrote:
Archit3110 wrote:
Bunuel wrote:
If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?

(A) 0.125
(B) 0.25
(C) 0.375
(D) 0.50
(E) 0.666


total fair chances ; 1/2*1/2*1/2 = 1/8 ; .125
and getting heads twice in 3 flips we have
HHT; HTH; THH ; 3 ways so .125*3 ; .375
IMO C


Hello, thanks for the solution.

Kindly explain why we have to consider 3 different scenarios for the flips.

I assumed that one flip is when we get either a head or a tail and that we have adequately covered the 3 consecutive flips by 1/2*1/2*1/2 = 1/8

Why then are we considering 3 different flips when the question hasn't explicitly told us that 3 different events took place?

Thanks


Hi

first, we calculate the probability of getting 3 heads = (1/2)^2 = 1/8 then we account for the order of heads in each toss HHT = 3!/2! = 3 therefore 1/8*3=3/8=0.375
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Re: If a coin has an equal probability of landing heads up or tails up eac [#permalink] New post   28 Apr 2021, 18:33
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If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?

(A) 0.125
(B) 0.25
(C) 0.375
(D) 0.50
(E) 0.666

Possibilities:

HHT
THH
HTH

Each possibility has a 1/2 x 1/2 x 1/2 = 1/8 chance of happening

1/8 + 1/8 + 1/8 = 3/8 = 0.375

C
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Re: If a coin has an equal probability of landing heads up or tails up eac [#permalink] New post   16 Oct 2022, 11:21
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Given that A fair coin is tossed three times, and we need to find what is the probability that the coin will land heads up exactly twice

Coin is tossed 3 times => Total number of cases = \(2^3\) = 8

Out of these 8 cases following are the cases in we will get exactly two heads
THH, HTH, HHT
=> 3 cases

=> Probability that the coin will land heads up exactly twice = \(\frac{3}{8}\) = 0.375

So, Answer will be C
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

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Re: If a coin has an equal probability of landing heads up or tails up eac [#permalink] New post   30 Dec 2023, 07:07
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