GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
On three consecutive flips of a coin, what is the probability that all
[#permalink]
20 Jan 2022, 06:14
20 Jan 2022, 06:14
Expert Reply
00:00
Question Stats:
68% (00:28) correct
31% (00:21) wrong based on 19 sessions
Hide Show timer Statistics
On three consecutive flips of a coin, what is the probability that all three produce the same result?
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: On three consecutive flips of a coin, what is the probability that all
[#permalink]
20 Jan 2022, 07:02
20 Jan 2022, 07:02
Carcass wrote:
On three consecutive flips of a coin, what is the probability that all three produce the same result?
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
APPROACH #1
P(3 identical flips) = P(1st flip is ANY side AND 2nd flip matches 1st flip AND 3rd flip matches 1st flip)
= P(1st flip is ANY side) x P(2nd flip matches 1st flip) x P(3rd flip matches 1st flip)
= 1 x 1/2 x 1/2
= 1/4
Answer: C
APPROACH #2
P(3 identical flips) = P(3 heads in a row OR 3 tails in a row)
= P(3 heads in a row) + P(3 tails in a row)
= P(1st flip is heads AND 2nd flip is heads AND 3rd flip is heads) + P(1st flip is tails AND 2nd flip is tails AND 3rd flip is tails)
= [P(1st flip is heads) x P(2nd flip is heads) x P(3rd flip is heads)] + [P(1st flip is tails) x P(2nd flip is tails) x P(3rd flip is tails)]
= [1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2]
1/8 + 1/8
= 1/4
Answer: C
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: On three consecutive flips of a coin, what is the probability that all
[#permalink]
18 Oct 2022, 10:04
18 Oct 2022, 10:04
1
We need to find On three consecutive flips of a coin, what is the probability that all three produce the same result?
Coin is tossed 3 times => Total number of cases = \(2^3\) = 8
Lets solve the problem using two methods
Method 1:
Out of the 8 cases there are only two cases in which all the outcomes are same. HHH and TTT.
=> Probability that all three produce the same result = \(\frac{2}{8}\) = \(\frac{1}{4}\)
So, Answer will be C
Method 2:
Let's find out the number of cases.
In the first toss we can get anything out of head or tail in 2 ways
In second toss we need to get the same value (head or tail) as we got in the first toss => 1 way
In third toss we need to get the same value (head or tail) as we got in the second toss => 1 way
=> Total number of ways = 2*1*1 = 2 ways
=> Probability that all three produce the same result = \(\frac{2}{8}\) = \(\frac{1}{4}\)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to Solve Probability with Coin Toss Problems
Coin is tossed 3 times => Total number of cases = \(2^3\) = 8
Lets solve the problem using two methods
Method 1:
Out of the 8 cases there are only two cases in which all the outcomes are same. HHH and TTT.
=> Probability that all three produce the same result = \(\frac{2}{8}\) = \(\frac{1}{4}\)
So, Answer will be C
Method 2:
Let's find out the number of cases.
In the first toss we can get anything out of head or tail in 2 ways
In second toss we need to get the same value (head or tail) as we got in the first toss => 1 way
In third toss we need to get the same value (head or tail) as we got in the second toss => 1 way
=> Total number of ways = 2*1*1 = 2 ways
=> Probability that all three produce the same result = \(\frac{2}{8}\) = \(\frac{1}{4}\)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to Solve Probability with Coin Toss Problems
