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

Question

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

pushpitkc · Answer

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)

JeffTargetTestPrep · Answer

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

EgmatQuantExpert · Answer

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   .

Regards,
Saquib
Quant Expert
e-GMAT

ScottTargetTestPrep · Answer

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

karenyip0911 · Answer

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.

BrushMyQuant · Answer

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!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Probability with Coin Toss Problems

https://www.youtube.com/watch?v=LRURv38kZw8

AshwinChadha · Answer

So, we have 1/2 chance that it lands on heads and 1/2 chance on tails.

However, since it doesn't specify which side we need, the first flip has a 1/1 probability (or 2/2) that it would either be a heads or a tails. 
Then on the second, third and fourth flips we have to get the same as the first flip which is 1/2 as depending on whether we got heads or tails we can only get that side. 
So, 1 * 1/2 * 1/2 * 1/2 = 1/2^3 = 1/8

Vibhatu · Answer

All four times may be H or T

H=1/16
T=1/16
H or T= 1/8

jassonadder · Answer

You want all four flips to show the same side — meaning either all heads (HHHH) or all tails (TTTT).

Now, the total number of possible outcomes when flipping four coins is 24 = 16.

Only two outcomes meet the condition:

HHHH

TTTT

So, the probability = (Number of favorable outcomes) ÷ (Total outcomes) = 2/16 = 1/8.

If you try this using a Flip 3 coins simulator (flipping three coins first and imagining a fourth flip), you’d notice it’s really rare to get all the same face — that’s why the probability is just 1/8.

Thus, the correct answer is (C) 1/8!

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards