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

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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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A fair coin is to be flipped four times. What is the probability that  [#permalink]

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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]

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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]

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New post 31 Jan 2018, 01:25
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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Saquib
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