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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If a fair coin is tossed six times, what is the probability  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: Senior Manager Joined: 20 May 2014
Posts: 282
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If a fair coin is tossed six times, what is the probability [#permalink]
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Question Stats: 18% (01:47) correct 81% (00:57) wrong based on 22 sessions
If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?

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

Kudos for correct solution.
[Reveal] Spoiler: OA Director Joined: 20 Apr 2016
Posts: 824
WE: Engineering (Energy and Utilities)
Followers: 10

Kudos [?]: 601  , given: 121

Re: If a fair coin is tossed six times, what is the probability [#permalink]
1
KUDOS
Bunuel wrote:
If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?

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

Kudos for correct solution.

The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n)

Let E = event of getting exactly 3 heads .

So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads}
=H H H T H T
H H H T T H
H H H T H H
H T H H H T
H T T H H H
H H T H H H
T H H H T T
T H H H T H
T H T H H H
T T H H H T
T T T H H H

So no. of favorable outcomes E =12
So the required probability = $$\frac{12}{64}$$ = $$\frac{3}{16}$$
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Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html Senior Manager Joined: 20 May 2014
Posts: 282
Followers: 18

Kudos [?]: 50  , given: 220

Re: If a fair coin is tossed six times, what is the probability [#permalink]
1
KUDOS
pranab01 wrote:
Bunuel wrote:
If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?

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

Kudos for correct solution.

The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n)

Let E = event of getting exactly 3 heads .

So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads}
=H H H T H T
H H H T T H
H H H T H H
H T H H H T
H T T H H H
H H T H H H
T H H H T T
T H H H T H
T H T H H H
T T H H H T
T T T H H H

So no. of favorable outcomes E =12
So the required probability = $$\frac{12}{64}$$ = $$\frac{3}{12}$$

Small typo there: 12/64 = 3/16, not 3/12.
Director Joined: 20 Apr 2016
Posts: 824
WE: Engineering (Energy and Utilities)
Followers: 10

Kudos [?]: 601 , given: 121

Re: If a fair coin is tossed six times, what is the probability [#permalink]
Bunuel wrote:

Small typo there: 12/64 = 3/16, not 3/12.

Yes you are right. I must take care next time Corrected
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Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html

Intern Joined: 15 Mar 2018
Posts: 32
Followers: 0

Kudos [?]: 8 , given: 1

Re: If a fair coin is tossed six times, what is the probability [#permalink]
pranab01 wrote:
Bunuel wrote:
If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?

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

Kudos for correct solution.

The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n)

Let E = event of getting exactly 3 heads .

So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads}
=H H H T H T
H H H T T H
H H H T H H
H T H H H T
H T T H H H
H H T H H H
T H H H T T
T H H H T H
T H T H H H
T T H H H T
T T T H H H

So no. of favorable outcomes E =12
So the required probability = $$\frac{12}{64}$$ = $$\frac{3}{16}$$

If you included H H H T H T, why are you not including H H H H H H ? there're exactly 3 Head consecutively in that arrangement. The answer is E
Manager Joined: 26 Jan 2018
Posts: 182
Followers: 0

Kudos [?]: 109 , given: 3

Re: If a fair coin is tossed six times, what is the probability [#permalink]
Other than putting the series on paper, is there is a better way to answer this question?
Intern Joined: 03 Apr 2018
Posts: 22
Followers: 0

Kudos [?]: 7 , given: 13

Re: If a fair coin is tossed six times, what is the probability [#permalink]
I’m also wondering like @mohan514 if there’s another place way?
Moderator  Joined: 18 Apr 2015
Posts: 5835
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Re: If a fair coin is tossed six times, what is the probability [#permalink]
Expert's post
No. I think no other way is possible or a shortcut.

Maybe @GreenlightTestPrep has more approaches.

Regards
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Intern Joined: 23 Sep 2018
Posts: 6
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Kudos [?]: 4 , given: 0

Re: If a fair coin is tossed six times, what is the probability [#permalink]
See there are 6 boxes to fill.
For such probs. always imagine things..try to visualize
If you fill first three by H (which stands for Head), only the possibility of 2 Hs exist that too after a gap of 1 box: HHHTHH== Max. 5 Hs expected
Now, similarly second way in which 3 Hs can come in a row: THHHTH==Thus only 4 Hs expected at max
similarly Third way: HTHHHT=4 Hs again at max
now Fourth way: HHTHHH= 5 Hs at max.

So do sum of individual possibilities of H in all 4 instances:
1: (1/2)^3 * (1/2)^2
2: (1/2)^3 * (1/2)
3: (1/2)^3 * (1/2)
4: (1/2)^3*(1/2)^2
Calculating===> (1/2)^4 {1/2+1+1+1/2}
===> 1/16*6/2===>3/16

Hope that Helps.

PS in probablities, there r no shortcuts please dont go by formulas rather try visualize imho Manager  Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 42 , given: 22

Re: If a fair coin is tossed six times, what is the probability [#permalink]
Expert's post
pranab01 wrote:
Bunuel wrote:
If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?

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

Kudos for correct solution.

The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n)

Let E = event of getting exactly 3 heads .

So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads}
=H H H T H T
H H H T T H
H H H T H H
H T H H H T
H T T H H H
H H T H H H
T H H H T T
T H H H T H
T H T H H H
T T H H H T
T T T H H H

I dont think this is correct.

So no. of favorable outcomes E =12
So the required probability = $$\frac{12}{64}$$ = $$\frac{3}{16}$$
Manager  Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 42 , given: 22

Re: If a fair coin is tossed six times, what is the probability [#permalink]
Expert's post
HEcom wrote:
pranab01 wrote:
Bunuel wrote:
If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?

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

Kudos for correct solution.

The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n)

Let E = event of getting exactly 3 heads .

So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads}
=H H H T H T
H H H T T H
H H H T H H
H T H H H T
H T T H H H
H H T H H H
T H H H T T
T H H H T H
T H T H H H
T T H H H T
T T T H H H

So no. of favorable outcomes E =12
So the required probability = $$\frac{12}{64}$$ = $$\frac{3}{16}$$

If you included H H H T H T, why are you not including H H H H H H ? there're exactly 3 Head consecutively in that arrangement. The answer is E

nope, because you need to get exaclty 3 heads, no more than that. Re: If a fair coin is tossed six times, what is the probability   [#permalink] 02 Jan 2019, 23:28
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