tmua.me Tau Paper 1 · Question 11

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tmua.me Tau Paper 1 · Q11

Paper 1ProbabilityNumber & counting

The numbers $X_1,\ldots,X_{12}$ consist of six $1$ s and six $-1$ s, with every choice of the six positive positions equally likely. Set $X_{13}=X_1$ , $X_{14}=X_2$ , and

Y_i=X_iX_{i+1}X_{i+2}\qquad(1\le i\le12).

What is the probability that exactly ten of the twelve numbers $Y_i$ are positive?

\dfrac1{77}

\dfrac6{77}

\dfrac3{77}

\dfrac1{154}

\dfrac2{77}

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