SOLUTION: (a) Among the three coins, one has heads on both the faces the second has tails on both the faces, and the third has a head on one face and a tail on the other. A coin chosen at ra

Algebra ->  Probability-and-statistics -> SOLUTION: (a) Among the three coins, one has heads on both the faces the second has tails on both the faces, and the third has a head on one face and a tail on the other. A coin chosen at ra      Log On


   

Question 1193277: (a) Among the three coins, one has heads on both the faces the second has tails on both the faces, and the third has a head on one face and a tail on the other. A coin chosen at random and tossed. The result is a head. What is the probability that the opposite face is a tail?
Answer by ikleyn(52855) About Me  (Show Source):
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(a) Among the three coins, one has heads on both the faces the second has tails on both the faces,
and the third has a head on one face and a tail on the other. A coin chosen at random and tossed.
The result is a head. What is the probability that the opposite face is a tail?
~~~~~~~~~~~~~~~~ 

We are given that 


    +------------------------------------------------------------+
    |   a coin is chosen at random from the 3 coins and tossed;  |
    |             the result is a head (H).    (*)               |
    +------------------------------------------------------------+


It means that the chosen coin is either HH-coin or HT-coin, but not TT-coin.


Then in this reduced set of coins (HH-coin,HT-coin) we have only two possibilities for the opposite side:


    H from HH-coin or T from HT-coin, each of these two 
        possibilities with the probability 1/2.


So, under the given condition (*), the probability to have the opposite side T is 1/2.    ANSWER

Solved.