(4). (a). You have a box with two fair coins and one two-headed coin in it. You
ID: 1891858 • Letter: #
Question
(4).(a). You have a box with two fair coins and one two-headed coin in it. You select one of the coins at random;
when you flip it, it shows heads. What is the probability that it is the two-headed coin?
(b). Now, suppose you flip the same coin a second time and again it shows heads. What is now the probability
that it is the two-headed coin?
(c). Now, suppose that you flip the same coin a third time and it shows heads. What is now the probability that
it is the two-headed coin?
(d). Now, suppose that once again you flip the same coin a fourth time and it shows tails. What is now the
probability that it is the two-headed coin?
Explanation / Answer
There are three components in the various streams (A, B, and C). Thus we can write an overall balance and component balances on two of the components (A and B, or B and C, or A and C). We could also write a component balance for all three components (A, B, and C) but not use the overall balance. Thus we could write three independent material balances.
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