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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

26 Dec 2012, 05:53

1

This post received KUDOS

16

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

72% (01:42) correct
28% (00:47) wrong based on 870 sessions

HideShow timer Statistics

The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

04 Jan 2013, 17:27

6

This post received KUDOS

1

This post was BOOKMARKED

Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2 H T T -> 3 * 1/2*1/2*1/2 T T T -> 1/2*1/2*1/2

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

16 Sep 2013, 11:09

caioguima wrote:

Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2 H T T -> 3 * 1/2*1/2*1/2 T T T -> 1/2*1/2*1/2

P = 3/8 + 3/8 + 1/8 = 7/8

Hi,

Kindly explain why it is 3* 1/2 * 1/2 * 1/2. According to my understanding, the prob of head is 1/2 and tail is 1/2. So HHT just has to be 1/2 * 1/2 * 1/2.. Isn't it? why multiply by 3? Kindly clarify.

Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2 H T T -> 3 * 1/2*1/2*1/2 T T T -> 1/2*1/2*1/2

P = 3/8 + 3/8 + 1/8 = 7/8

Hi,

Kindly explain why it is 3* 1/2 * 1/2 * 1/2. According to my understanding, the prob of head is 1/2 and tail is 1/2. So HHT just has to be 1/2 * 1/2 * 1/2.. Isn't it? why multiply by 3? Kindly clarify.

The point is that two heads and a tail can occur in three ways: HHT, HTH, THH. The probability of each case is 1/2*1/2*1/2.

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

20 Nov 2013, 04:41

Bunuel wrote:

Walkabout wrote:

The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

Bunuel, would you mind explaining how you find the power to which you have to raise? What if e.g. there is a bag with three marbles, blue, red and yellow. Now the question is e.g. "What is the probabilty to get a blue marble on at least 1 try if you try 4 times" (putting the marbles back all the time).

Would it be P(at least 1 blue marble) = 1 - P(none blue) = 1 - (2/3)^4 ??

The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

Bunuel, would you mind explaining how you find the power to which you have to raise? What if e.g. there is a bag with three marbles, blue, red and yellow. Now the question is e.g. "What is the probabilty to get a blue marble on at least 1 try if you try 4 times" (putting the marbles back all the time).

Would it be P(at least 1 blue marble) = 1 - P(none blue) = 1 - (2/3)^4 ??

Thanks for your explanation!

Yes, that's correct, the power must be the number of tries.

For the original question: P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2*1/2*1/2)= 1 - (1/2)^3 = 7/8.

For your example: P(at least 1 blue) = 1 - P(no blue) = 1- (2/3*2/3*2/3*2/3) = 1- (2/3)^4.

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

28 Nov 2014, 10:48

1

This post received KUDOS

First thing to do is to come up with the total number of possible outcomes: The coin is tossed 3 times and there is an equal probability that the coin will turn up heads or tail on each toss (which means that each toss has only two possible outcomes) _ _ _ 2*2*2=2^3=8 Multiply the number of possible outcomes per toss to arrive at the total number of possible outcomes. If the Question would state that the coin is to be tossed four times, the total number of possible outcomes would simply imply another multiplication by 2 or 2^4 which is 16.

Next step is to find the number of scenarios that fulfill the condition the Question stem asks for. (At least one tail) One can easily recognize that ALL scenarios BUT ONE will include at least one tail. I am talking about the scenario in which all three tosses result in heads. --> HHH So 7 out of 8 scenarios will include at least one tail. THH, HTH, HHT etc… This is already your final answer. P(at least one tail) = 7/8

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

12 Dec 2015, 03:14

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

07 Jul 2016, 09:16

Walkabout wrote:

The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8 (B) 1/2 (C) 3/4 (D) 7/8 (E) 15/16

In this problem, there are only two events that could occur for the 3 coin flips. Either the coin will land on tails zero times, or the coin will land on tails at least one time. (Remember that the phrase "at least one time" means "one or more."

Writing this in a probability statement yields:

P(landing on tails at least 1 time) + P(landing on tails zero times) = 1

Thus, we can say:

P(landing on tails at least 1 time) = 1 - P(landing on tails zero times)

Since we are tossing the coin 3 times, the outcome of zero tails in 3 tosses is the same as getting heads on all 3 tosses. We can calculate the probability of zero tails in 3 tosses as the probability of 3 heads in 3 tosses:

½ x ½ x ½ =1/8

Plugging this into our formula we have:

P(landing on tails at least 1 time) = 1 – 1/8

P(landing on tails at least 1 time) = 7/8

Answer is D.
_________________

Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...