suppose three coins are lying on a table, two of them with heads facing up and one with tails facing up . one coin is chosen at random and flipped. what is the probability that after the flip the majority of coins ( i.e. at least two of them) will have _?_ facing up
We start with 1H,2H,3T
A. We choose 1H to flip 1/3 of the time
1. 1H doesn't change and we end up with 1H,2H,3T
1/2 of 1/3 of the time or 1/6th of the time
2. 1H changes and we end up with 1T,2H,3T
1/2 of 1/3 of the time or 1/6th of the time
B. We choose 2H to flip 1/3 of the time
1. 2H doesn't change and we end up with 1H,2H,3T
1/2 of 1/3 of the time or 1/6th of the time
2. 2H changes and we end up with 1H,2T,3T
1/2 of 1/3 of the time or 1/6th of the time
C. We choose 3T to flip 1/3 of the time
1. 3T doesn't change and we end up with 1H,2H,3T
1/2 of 1/3 of the time or 1/6th of the time
2. 3T changes and we end up with 1H,2H,3H
1/2 of 1/3 of the time or 1/6th of the time
what is the probability that after the flip the majority of coins ( i.e. at
least two of them) will have HEADS facing up.
That will be P(A1 or B1 or C1 or C2) = 1/6 times 4 = 4/6 or 2/3.
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what is the probability that after the flip the majority of coins ( i.e. at
least two of them) will have TAILS facing up.
That will be P(A2 or B2) = 1/6 times 2 = 2/6 or 1/3.
Edwin
