Die A has 4 red and 2 white faces, whereas die B has 2 red and 4 white faces. A fair coin is flipped once. If it lands on heads, the game continues with die A; if it lands on tails, then die B is to be used. Find the probability of red at any throw
Let's say the coin landed on heads, which is a 1/2 chance.
Then the chance of it being red is 4/6 = 2/3.
Therefore, the total so far is 1/2*2/3 = 1/3
Now if the coin landed on tails, 1/2 chance
Red is 2/6 = 1/3
1/2*1/3 = 1/6
Total probability - 1/3 + 1/6 = 1/2
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