There are three coins. One coin is having tails on both faces, another is a biased coin that comes up tails 70% of the time and the third is an unbiased coin. One of the coins is chosen at random and tossed. Find the probability that it shows tail.
Answer (1)
Student Expert
21st Dec, 2020
Hey!
the question is of baye's theorem.
Let us say that "E" is the event that the chosen coin always shows tail.
now, let E1 , E2 & E3 are the coins which shows tail on both sides, biased coin (70%) and unbiased coin respectively.
So, p (E1)=p(E2)=p(E3)=1/3 (as the chosen coin can be any of the three, so the probability of each coin to be chosen is 1/3).
Now, p(E/E1)= 1, p(E/E2) = 70/100 and p(E/E3)= 1/2 -----(1)
By Baye's theorem
p (E1/E) = [p(E/E1)p(E1)] / [ {p(E/E1)p(E1) } + {p(E/E2)p(E2)} + {p(E/E3)p(E3)} ]
by putting the values from equation (1)
and solving, we get,
p(E/E1) = 5/11
thankyou
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