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A fair coin is to be flipped four times. What is the probability that

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Bunuel
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A fair coin is to be flipped four times. What is the probability that [#permalink] New post   29 Jan 2018, 05:42
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A fair coin is to be flipped four times. What is the probability that the coin will land on the same side on all four flips?

(A) 1/32
(B) 1/16
(C) 1/8
(D) 1/4
(E) 1/2
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C
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Re: A fair coin is to be flipped four times. What is the probability that [#permalink] New post   30 Jan 2018, 11:17
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Bunuel wrote:
A fair coin is to be flipped four times. What is the probability that the coin will land on the same side on all four flips?

(A) 1/32
(B) 1/16
(C) 1/8
(D) 1/4
(E) 1/2


We have two options: all heads or all tails.

The probability of all heads is (1/2)^4 = 1/16, and the probability of all tails is also 1/16, so the total probability is 1/16 + 1/16 = 2/16 = 1/8.

Answer: C
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A fair coin is to be flipped four times. What is the probability that [#permalink] New post   31 Jan 2018, 01:25
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Bunuel wrote:
A fair coin is to be flipped four times. What is the probability that the coin will land on the same side on all four flips?

(A) 1/32
(B) 1/16
(C) 1/8
(D) 1/4
(E) 1/2


Solution



    • We are given that a fair coin is flipped four times.

      o Each time, we will get either a head or a tail.
      o Thus, total possible cases \(= 2 * 2 * 2 * 2 = 16\)
    • We need to find the probability that the coin will land on the same side on all four flips.

      o This is possible only when all the four time, we get all HEADs (HHHH) or all TAILs (TTTT)

      o Thus, total favorable cases \(= 1 + 1 = 2\)

    • Thus, the probability \(= \frac{Favorable Cases}{Total Cases} = \frac{2}{16} = \frac{1}{8}\)

The correct answer is Option C.

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A fair coin is to be flipped four times. What is the probability that [#permalink] New post   29 Jan 2018, 06:22
Bunuel wrote:
A fair coin is to be flipped four times. What is the probability that the coin will land on the same side on all four flips?

(A) 1/32
(B) 1/16
(C) 1/8
(D) 1/4
(E) 1/2


There are two possibilities in which the coin will land - Head or Tail
The probability of the coin landing on either side is \(\frac{1}{2}\)

We have been asked to find the probability that the coin will land on the same side all 4 times.

Probability is \(\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}\) that the coin lands a head every time
Probability is \(\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}\) that the coin lands a tail every time

Hence, total probability is \(2*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2} = \frac{1}{8}\)(Option C)
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Re: A fair coin is to be flipped four times. What is the probability that [#permalink] New post   21 Jun 2019, 11:34
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Bunuel wrote:
A fair coin is to be flipped four times. What is the probability that the coin will land on the same side on all four flips?

(A) 1/32
(B) 1/16
(C) 1/8
(D) 1/4
(E) 1/2



The probability of all heads is (1/2)^4 = 1/16, and the probability of all tails is 1/16. So, the probability of the coin landing on the same side on all four flips is 2/16 = 1/8.

Alternate solution:

Which side the coin lands the first time doesn’t matter (so the probability is 1), but there is only a ½ chance on each successive flip for the coin to land on the same side as the first time. Therefore, the probability that the coin will land on the same side on all four flips is:

1 x ½ x ½ x ½ = 1/8

Answer: C
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Re: A fair coin is to be flipped four times. What is the probability that [#permalink] New post   21 Jun 2021, 22:28
Hi all,

does anyone know how to use the combination formula to solve this question?

= # of ways of selection x (1/2*1/2*1/2*1/2)
= 4C1 * 1/16

but the answer is not correct, can someone please let me know what is incorrect here? thanks much.
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Re: A fair coin is to be flipped four times. What is the probability that [#permalink] New post   04 Oct 2022, 05:16
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Given that A fair coin is to be flipped four times and We need to find What is the probability that the coin will land on the same side on all four flips?

Coin is tossed 4 times => Total number of cases = \(2^4\) = 16

Coin lands on the same side = Getting 4 Tails or Getting 4 Heads

=> P(4H or 4T) = \(\frac{2}{16}\) (As there is two cases out of 16 where we get 4H or 4T)
= \(\frac{1}{8}\)

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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gmatclubot
Re: A fair coin is to be flipped four times. What is the probability that [#permalink]
04 Oct 2022, 05:16
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