GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 04:24

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58319
A fair coin is to be flipped four times. What is the probability that  [#permalink]

### Show Tags

29 Jan 2018, 05:42
2
6
00:00

Difficulty:

35% (medium)

Question Stats:

52% (00:42) correct 48% (00:37) wrong based on 86 sessions

### HideShow timer Statistics

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

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12
A fair coin is to be flipped four times. What is the probability that  [#permalink]

### Show Tags

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)
_________________
You've got what it takes, but it will take everything you've got
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: A fair coin is to be flipped four times. What is the probability that  [#permalink]

### Show Tags

30 Jan 2018, 11:17
2
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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
A fair coin is to be flipped four times. What is the probability that  [#permalink]

### Show Tags

31 Jan 2018, 01:25
1
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.

Regards,
Saquib
Quant Expert
e-GMAT
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: A fair coin is to be flipped four times. What is the probability that  [#permalink]

### Show Tags

21 Jun 2019, 11:34
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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: A fair coin is to be flipped four times. What is the probability that   [#permalink] 21 Jun 2019, 11:34
Display posts from previous: Sort by