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02 Mar 2013, 09:02
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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
A. 2/5
B. 1/2
C. 4/5
D. 2/3
E. 3/4
03 Mar 2013, 05:27
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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
@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
pariearth
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..
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
