Die I has 4 red and 2 white faces and die I has 2 red and 4 white faces. A coin is flipped once. If head appears, the game continues by flipping die I, and if tail appears, then die II is used. The probability of getting a red face at any throw is:

Using the law of total probability, the total chance of getting a red face equals the probability of flipping heads times the probability of red on die one, plus the probability of flipping tails times the probability of red on die two. The probability of heads or tails is 1/2, the probability of red on die one is 4/6, and the probability of red on die two is 2/6. This calculation gives (1/2 times 4/6) plus (1/2 times 2/6), which equals 1/2.

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