Apr 24 08:00 AM PDT  09:00 AM PDT Join the Live Chat April 24th at 8 am PT. Learn the best strategies for acing the Verbal section. From Sentence Correction tactics to 3 keys for solving Reading Comprehension questions and tips for Critical Reasoning questions. Apr 24 08:00 PM EDT  09:00 PM EDT Maximize Your Potential: 5 Steps to Getting Your Dream MBA Part 3 of 5: Key TestTaking Strategies for GMAT. Wednesday, April 24th at 8 pm ET Apr 25 10:00 PM PDT  11:00 PM PDT Join an exclusive workshop for GMAT Club members and learn how to cut your preparation time by 50% and still reach a 700+ on the GMAT. Limited for the first 99 registrants. Register today! Apr 27 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Apr 28 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Apr 29 08:00 AM PDT  09:00 AM PDT Join a free live webinar and learn timemanagement tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! May 01 10:00 PM PDT  11:00 PM PDT Target Test Prep is kicking off spring with a fresh giveaway contest! For a limited time, you have a chance to win 4 months of full, FREE access to our 5star rated GMAT Quant course.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 29 May 2008
Posts: 109

What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
17 Jun 2009, 06:10
Question Stats:
60% (01:57) correct 40% (02:11) wrong based on 105 sessions
HideShow timer Statistics
What is the probability of tossing a coin five times and having heads appear at least two times? A) 1/32 B) 1/16 C) 15/16 D) 13/16 E) 7/8
Official Answer and Stats are available only to registered users. Register/ Login.



Senior Manager
Joined: 08 Jan 2009
Posts: 288

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
17 Jun 2009, 06:54
If 'n' coins are tossed there will nc0 outcomes in which n coins will show head nc1 outcomes in which 1 head will appear and so on
Here 5 coins are tossed so the total outcomes = 2 ^5 = 32
Outcomes in which atleast 2 heads will appear = 32  5c0  5c1 = 26
Prob atleast two heads will appear = 26/32 = 13/16



Manager
Joined: 29 May 2008
Posts: 109

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
17 Jun 2009, 07:52
Sorry man, but I dont get this
If 'n' coins are tossed there will nc0 outcomes in which n coins will show head nc1 outcomes in which 1 head will appear and so on
Would you please explain me better,
Is there any other way easier
YOu are correct with your answer but I cant understand it yet
HELP!
hehe



Senior Manager
Joined: 08 Jan 2009
Posts: 288

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
17 Jun 2009, 20:00
Let take an example if 2 coins are tossed the total outcome= 2 ^n = 2 ^2 = 4 ( HH,HT,TH,TT)
The number of outcome 0 head can appear = nc0 = 2c0 = 1 ( TT ) The number of outcome 1 head can appear = nc1 = 2c1 = 2 (HT,TH) The number of outcome 2 head can appear = nc2 = 2c2 = 1 (HH)
The same rule i have generalised and put below. U need to follow the same for 5 coins.
I have proved it above for 2 coins so same for other values of n.
Hope u got it.



Manager
Joined: 25 May 2009
Posts: 131
Concentration: Finance
GMAT Date: 12162011

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
18 Jun 2009, 08:31
Here is another way to do it, although longer, but it may help you:
Total outcomes = 2^5 = 32 Outcomes which 2 heads appear = 5C2 = 5!/2!3! = 10 Outcomes which 3 heads appear = 5C3 = 5!/3!2! = 10 Outcomes which 4 heads appear = 5C4 = 5!/4!1! = 5 Outcomes which 5 heads appear = 5C5 = 5!/5!0! = 1
Sum selected outcomes = 10+10+5+1 = 26
Selected outcomes / total outcomes = 26/32 = 13/16



Manager
Joined: 29 May 2008
Posts: 109

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
18 Jun 2009, 09:33
Thank you man ,
Now it did Help
I don't know how to get better in probability it is painful for me
DO you know if Prob, combinatorics and perm show very often on the GMAT?



Manager
Joined: 25 May 2009
Posts: 131
Concentration: Finance
GMAT Date: 12162011

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
18 Jun 2009, 12:09
I haven't taken the exam yet, but in my practice exams they see to show up pretty regularly (GMATPrep) and they are in the OG books (which are older GMAT questions). If I were you I would keep working on them, it took me a while to grasp the concepts but there are a lot of great posts on here which will help you as well as external links that people have posted for additional help.



Manager
Joined: 29 May 2008
Posts: 109

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
22 Jun 2009, 07:23
I finally knew how to solve this onein an easier way
first of all lets get what we dont want...
I don't want TAILS so
T T T T T = 1/32
and I dont want one head either
H T T T T = 5/32
SO I dont want either a 1/32 or 5/32
so we get 6/32
and now 32/32  6/32 = 26/32
getting final answer 13/16
Very interesting question
What do you think?



Intern
Joined: 19 Mar 2010
Posts: 10
Location: San Diego, CA
Schools: UCLA Anderson

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
24 Mar 2010, 14:16
TheRob wrote: I finally knew how to solve this onein an easier way
first of all lets get what we dont want...
I don't want TAILS so
T T T T T = 1/32
and I dont want one head either
H T T T T = 5/32
SO I dont want either a 1/32 or 5/32
so we get 6/32
and now 32/32  6/32 = 26/32
getting final answer 13/16
Very interesting question
What do you think? I agree. One way to look at these "at least" probability questions is to take 1  P(event not happening) In this case, the probability of at least two heads is 1  P(less than two heads), which means 1  [P(zero heads) + P(one head)] which is = 1  (5C0/32 + 5C1/32)= 1  (1/32 + 5/32)= 26/3213/26answer D



Intern
Joined: 29 Oct 2009
Posts: 43

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
25 Mar 2010, 02:19
In questions involving Coins, its always safe to use to combinations which are less in number...
for example in question above we need to find out probability of at least 2 heads, which also means that we can just find probability when number of heads <2 i.e. no heads at all or just 1 head...then whatever is the outcome we just need to subtract it from 1.
total outcome = 1  P(no heads+ 1head)



Intern
Joined: 17 Dec 2009
Posts: 24

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
25 Mar 2010, 14:39
tkarthi4u, unless I'm doing this wrong that method doesn't work on this example: Let's say 5 coins are tossed, what is the probablility that 3 will be tails?
Total outcome = 32
Outcome of 3 tails appearing = 325C05C15C2 = 16 16/32 = 1/2 but that isn't the correct answer
Please advise.



Senior Manager
Joined: 21 Jul 2009
Posts: 316
Schools: LBS, INSEAD, IMD, ISB  Anything with just 1 yr program.

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
26 Mar 2010, 16:35
Friends, seems like there is a lot of confusion regarding questions of this type. This question is a typical binomial probability question. Situations where there are only two possibilities that can happen, a coin is flipped and the outcome is either a heads or tails. A baby is born, and the possibility is a boy or a girl. This can however be extended to situations when a dice is rolled. Probability of getting a particular number against probability of not getting the desired number. Now, let's extrapolate the situation to multiple trials. Let's say n trials were made, and we define a particular occurrence as a success event, the nonoccurrence is thus a failure event, and r such successes are counted. The probability of each success event is p, and therefore, the probability of each failure event is q = 1p. We need to identify the probability of r successes in n trials. This particular situation was studied by a famous mathematician by the name Bernoulli. Hence, these are called Bernoulli's trials. And the formula goes  [nCr]*[p^(r)]*[q^(nr)]. When a coin is flipped 5 times, probability of 2 heads/tails, note that the success events can be random, the order of success events is not considered in this situation, would be [5C2]*[(1/2)^(2)]*[(1/2)^(3)] = 5/16. Consider a dice is rolled 8 times, probability of getting a 4 exactly 3 times would be [8C3]*[(1/6)^(3)]*[(5/6)^(5)]. Now, occurrence of a particular event at least r times would mean, nonoccurrence of the event for nr times. We can count accordingly, depending on values for n and r. Sum of all probabilities of desired events, r ranging from 0 to n, will be equal to 1.
_________________
I am AWESOME and it's gonna be LEGENDARY!!!



Manager
Joined: 01 Feb 2010
Posts: 225

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
27 Mar 2010, 04:25
BarneyStinson wrote: Friends, seems like there is a lot of confusion regarding questions of this type.
This question is a typical binomial probability question. Situations where there are only two possibilities that can happen, a coin is flipped and the outcome is either a heads or tails. A baby is born, and the possibility is a boy or a girl. This can however be extended to situations when a dice is rolled. Probability of getting a particular number against probability of not getting the desired number.
Now, let's extrapolate the situation to multiple trials. Let's say n trials were made, and we define a particular occurrence as a success event, the nonoccurrence is thus a failure event, and r such successes are counted. The probability of each success event is p, and therefore, the probability of each failure event is q = 1p. We need to identify the probability of r successes in n trials.
This particular situation was studied by a famous mathematician by the name Bernoulli. Hence, these are called Bernoulli's trials. And the formula goes  [nCr]*[p^(r)]*[q^(nr)].
When a coin is flipped 5 times, probability of 2 heads/tails, note that the success events can be random, the order of success events is not considered in this situation, would be [5C2]*[(1/2)^(2)]*[(1/2)^(3)] = 5/16.
Consider a dice is rolled 8 times, probability of getting a 4 exactly 3 times would be [8C3]*[(1/6)^(3)]*[(5/6)^(5)].
Now, occurrence of a particular event at least r times would mean, nonoccurrence of the event for nr times. We can count accordingly, depending on values for n and r. Sum of all probabilities of desired events, r ranging from 0 to n, will be equal to 1. Nice explanation regarding Binomial distribution.



Senior Manager
Joined: 20 Aug 2015
Posts: 388
Location: India

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
12 Nov 2015, 04:17
TheRob wrote: What is the probability of tossing a coin five times and having heads appear at least two times?
A) 1/32 B) 1/16 C) 15/16 D) 13/16 E) 7/8 The best and the fastest way to do a problem which talks about at least scenarios is to subtract the probability of that scenario happening from the total frequency. Note: The probability of the scenario that you have to subtract will almost always be of a small number of cases.Coming to this question: Total cases = 2^5 = 32 Case 1: No heads = 5C0 = 1 Case 2: 1 heads = 5C1 = 5 Hence The cases which we need are 32  1  5 = 26 Probability = 26/32 = 13/16 Option D



Intern
Joined: 10 Dec 2014
Posts: 45
Concentration: Marketing
WE: Marketing (Manufacturing)

Re: What is the probability of tossing a coin five times and having heads
[#permalink]
Show Tags
10 Jul 2017, 10:00
We need to calculate the probability of having at least 2 heads after tossing a coin 5 times.
=> Calculate the probability of having 0 head and probability of having 1 head, then deduct that from 1 to find the answer.
Probability of having 0 head (TTTTT)= [(1/2)^5] = 1/32 Probability of having 1 head = [(1/2)^5]*5(positions of head) = 5/32
=> Probability of having at least 2 heads after tossing 5 coins = 1  1/32 5/32 = 26/32 = 23/32




Re: What is the probability of tossing a coin five times and having heads
[#permalink]
10 Jul 2017, 10:00






