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Conditional on the first toss being odd, either 1) the second toss is the same as the first (the 1/6 part) or 2) the second is an odd number different from the first toss (with probability 2/6=1/3) after which the sum starting with the second toss has to be odd (probability 1-q) or 3) the second is an even number (probability 1/2) after which the sum starting with the second toss is odd (probability 1-p)also note that p+q is not 1.
Conditional on the first toss being odd, either 1) the second toss is the same as the first (the 1/6 part) or 2) the second is an odd number different from the first toss (with probability 2/6=1/3) after which the sum starting with the second toss has to be odd (probability 1-q) or 3) the second is an even number (probability 1/2) after which the sum starting with the second toss is odd (probability 1-p)
also note that p+q is not 1.
