There are three coins. They have chances 0.4, 0.6 and 0.8 respectively of showing heads. One...
There are three coins. They have chances 0.4, 0.6 and
0.8 respectively of showing heads. One of
these three coins is chosen at random and flipped.
(a) What is the chance that the coin chosen is the coin with
probability equal to .4 of showing
heads and a head shows up after the flip?
(b) What is the chance that the coin, when flipped, shows a
head?
(c) Given that the coin, when flipped, shows a head, what is the
chance that the coin is the coin
with probability equal to 0.4 of showing heads?
Homework Answers
Let us denote A, B , and C be the first , second and third coins with probabilities of showing heads as 04, 06, 08 respectively.
a) Here we want to find P( A and H ) = P( A) * P( H|A) = (1/3) * 0.4 = 0.133333
b) Here we want to find P( H ) = P(H and A) + P(H and B) + P(H and C) = 0.4 *(1/3) + 0.6*(1/3) + 0.8* (1/3)
= (1/3)*(0.4 + 0.6 +0.8) = (1/3) *1.8 = 0.6
c) Here we want to find P(A | H)
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