Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 03 May 2015, 07:13

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 3

Kudos [?]: 735 [0], given: 0

The probability is 1/2 that a certain coin will turn up head [#permalink]  26 Dec 2012, 05:53
5
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

74% (01:42) correct 26% (00:40) wrong based on 445 sessions
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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27168
Followers: 4225

Kudos [?]: 40918 [3] , given: 5576

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]  26 Dec 2012, 05:59
3
KUDOS
Expert's post
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

P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.

_________________
Manager
Joined: 02 Jan 2013
Posts: 57
GMAT 1: 750 Q51 V40
GPA: 3.2
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 36 [4] , given: 2

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]  04 Jan 2013, 17:27
4
KUDOS
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
Intern
Joined: 27 Feb 2013
Posts: 4
Followers: 0

Kudos [?]: 1 [0], given: 5

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]  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.
Math Expert
Joined: 02 Sep 2009
Posts: 27168
Followers: 4225

Kudos [?]: 40918 [0], given: 5576

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]  16 Sep 2013, 11:17
Expert's post
2
This post was
BOOKMARKED
abhinaya wrote:
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.

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.

Theory on probability problems: math-probability-87244.html

All DS probability problems to practice: search.php?search_id=tag&tag_id=33
All PS probability problems to practice: search.php?search_id=tag&tag_id=54

Tough probability questions: hardest-area-questions-probability-and-combinations-101361.html

_________________
Manager
Joined: 21 Oct 2013
Posts: 194
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Followers: 0

Kudos [?]: 18 [0], given: 19

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]  20 Nov 2013, 04:41
Bunuel 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

P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.

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 ??

Math Expert
Joined: 02 Sep 2009
Posts: 27168
Followers: 4225

Kudos [?]: 40918 [1] , given: 5576

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]  20 Nov 2013, 04:51
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
unceldolan wrote:
Bunuel 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

P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.

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 ??

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.

Hope it's clear.
_________________
Manager
Joined: 21 Oct 2013
Posts: 194
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Followers: 0

Kudos [?]: 18 [0], given: 19

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]  20 Nov 2013, 05:35
ok great thank you!
Intern
Joined: 25 Sep 2014
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: The probability is 1/2 that a certain coin will turn up head [#permalink]  28 Nov 2014, 10:48
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…
Re: The probability is 1/2 that a certain coin will turn up head   [#permalink] 28 Nov 2014, 10:48
Similar topics Replies Last post
Similar
Topics:
The probability is 1/2 that a certain coin will turn up 3 17 Nov 2013, 17:39
6 The probability is 0.6 that an “unfair” coin will turn up 7 02 Nov 2009, 04:51
The probability is that a certain coin will turn up heads 2 14 Jul 2007, 17:25
The probability is .5 that a certain coin will turn up heads 2 25 Nov 2006, 15:14
If a coin has a probability of landing heads up or tails 2 26 Dec 2005, 18:06
Display posts from previous: Sort by