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A box contains four coins, of which two coins have heads on

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A box contains four coins, of which two coins have heads on [#permalink] New post 02 Mar 2013, 08:02
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A box contains four coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.

A. 2/5
B. 1/2
C. 4/5
D. 2/3
E. 3/4
[Reveal] Spoiler: OA
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 02 Mar 2013, 18:24
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How many ways can you get heads with a two-headed coin? There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)

How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)

Therefore probability = 4/5

Option C
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 02 Mar 2013, 19:33
I would say
There are total 4 coins of which only 2 coins have both heads, so the answer is 2/4 = 1/2.
Not sure whether each head can be treated separately...

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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 02 Mar 2013, 23:20
GyanOne wrote:
How many ways can you get heads with a two-headed coin? There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)

How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)

Therefore probability = 4/5

Option C


Can you please explain this -
If I have already tossed the coin and have got a head then how is the probability of getting another head on the other face = 4/5 ??
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 02 Mar 2013, 23:37
pariearth wrote:
A box contains four coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face(hidden face) of the coin tossed is also a head.
A. 2/5
B. 1/2
C. 4/5
D. 2/3
E. 3/4

Guys need a detailed explaination here..


If head comes out of toss, then the coin is among: two coins that have heads on both their faces and the normal one.

Total possible outcomes: 3 (HHT)
Possible head : 2 (ruling out the tail for the normal coin)

Probability = 2/3
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 03 Mar 2013, 04:27
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Guys, the question says that a coin is picked at random and then tossed. This means that a coin is picked up from among the four available, and without determining what kind of coin it is, this coin is tossed. The outcome of this toss is heads.

@nt2010: The outcome of the toss (heads), can be obtained in five different ways, so you need to consider each head separately.

@pariearth: What we are trying to do is given that the toss yielded a head, find out if the coin is two-headed or not.

@ConnectTheDots: We are considering just one toss of the coin. The set of outcomes you have described does not come into the picture at all.

Let me try and offer you another explanation. Once we toss one coin at random, we see that the outcome is heads. We are trying to determine if this coin is two-headed. How many ways could we have got this heads by tossing a coin? Five ways, because this could be either of the heads of the two-headed coins, or the one heads on the fair coin. From these five ways, what are the number of ways that this heads would be from a two-headed coin? There are four ways to get heads from a two-headed coin (two from the first two-headed coin and two from the second).

Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 03 Mar 2013, 08:18
Thank you gyanOne.

What is the source of this question?
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 03 Mar 2013, 21:21
Nicely xplaind..+1 2u :)
GyanOne wrote:
Guys, the question says that a coin is picked at random and then tossed. This means that a coin is picked up from among the four available, and without determining what kind of coin it is, this coin is tossed. The outcome of this toss is heads.

@nt2010: The outcome of the toss (heads), can be obtained in five different ways, so you need to consider each head separately.

@pariearth: What we are trying to do is given that the toss yielded a head, find out if the coin is two-headed or not.

@ConnectTheDots: We are considering just one toss of the coin. The set of outcomes you have described does not come into the picture at all.

Let me try and offer you another explanation. Once we toss one coin at random, we see that the outcome is heads. We are trying to determine if this coin is two-headed. How many ways could we have got this heads by tossing a coin? Five ways, because this could be either of the heads of the two-headed coins, or the one heads on the fair coin. From these five ways, what are the number of ways that this heads would be from a two-headed coin? There are four ways to get heads from a two-headed coin (two from the first two-headed coin and two from the second).

Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 03 Mar 2013, 21:30
nt2010 wrote:
What is the source of this question?


This is from my not-so-famous tution class' study material.
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 03 Mar 2013, 22:25
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pariearth wrote:
A box contains four coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face(hidden face) of the coin tossed is also a head.
A. 2/5
B. 1/2
C. 4/5
D. 2/3
E. 3/4

Guys need a detailed explaination here..


You can use the conditional probability concept here. You need to find the probability that the coin you tossed was a two-heads coin given that you got heads.

P(A given B) = P(A)/P(B)

P(A) = P(Two heads coins) = 2/4 = 1/2 (since 2 of the 4 coins have two heads)
P(B) = P(Getting heads on flipping a coin) = 5/8 (you have 5 heads and 3 tails in total on the 4 coins)

P(A given B) = (1/2)/(5/8) = 4/5

For more on conditional probability, check: http://www.veritasprep.com/blog/2012/02 ... onditions/
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 04 Mar 2013, 11:44
@pariearth.....you are certainly welcome. Do let us know if you face any further difficulty in understanding this concept. The important part of a probability problem is always setting it up by first understanding what is being asked.
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 04 Mar 2013, 16:09
Expert's post
pariearth wrote:
A box contains four coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.

A. 2/5
B. 1/2
C. 4/5
D. 2/3
E. 3/4


More questions on conditional probability to practice:
if-ben-were-to-lose-the-championship-m07q12-75695.html
given-a-bag-with-2-black-balls-and-3-white-balls-126223.html
say-you-have-5-coins-1-coin-has-heads-on-both-sides-and-the-91232.html

Hope it helps.
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Re: A box contains four coins, of which two coins have heads on [#permalink] New post 24 Apr 2014, 07:54
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Re: A box contains four coins, of which two coins have heads on   [#permalink] 24 Apr 2014, 07:54
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