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

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

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

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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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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.

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

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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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A fair coin is to be flipped four times. What is the probability that   [#permalink] 31 Jan 2018, 01:25
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