Dice sequence: how many neighboring pairs match?

Question

You roll a fair six-sided die 12 times and write the results in a row. On average, how many of the 11 neighboring pairs show the same value on both rolls?

Accepted Answer

Twelve rolls make 11 neighboring pairs. Put one indicator on each pair and add. Fix a neighboring pair of rolls. The second roll matches the first only if it lands on that exact face, which happens with probability 	frac16: P(	ext{a given pair matches}) = \frac16. Let Xi = 1 if neighboring pair i matches; E[Xi] = 	frac16. With 11 pairs, E[	ext{matching pairs}] = 11 	imes \frac16 = \frac{11}{6} \approx 1.833. Takeaway. The condition on each neighboring pair sets its probability: matching faces on two dice happen with probability 	frac16, so 11 pairs average 	frac{11}{6} matches. Lineari…

Dice sequence: how many neighboring pairs match?

Your answer

More Probability questions