Standard +0.3 This is a binomial probability question requiring students to recognize that D depends on the difference between heads and tails, calculate P(D=0), P(D=2), P(D=4), P(D=6), and identify the maximum. While it requires understanding of the random walk setup and systematic calculation of several probabilities, it's a straightforward application of binomial distribution with no novel insight needed—slightly easier than average for A-level.
14 A counter is initially at point \(O\) on the \(x\)-axis. A fair coin is thrown 6 times. Each time the coin shows heads, the counter is moved one unit in the positive \(x\)-direction. Each time the coin shows tails, the counter is moved one unit in the negative \(x\)-direction. The final distance of the counter from \(O\), in either direction, is denoted by \(D\).
Determine the most probable value of \(D\).
\section*{END OF QUESTION PAPER}
\section*{OCR
Oxford Cambridge and RSA}
14 A counter is initially at point $O$ on the $x$-axis. A fair coin is thrown 6 times. Each time the coin shows heads, the counter is moved one unit in the positive $x$-direction. Each time the coin shows tails, the counter is moved one unit in the negative $x$-direction. The final distance of the counter from $O$, in either direction, is denoted by $D$.
Determine the most probable value of $D$.
\section*{END OF QUESTION PAPER}
\section*{OCR \\
Oxford Cambridge and RSA}
\hfill \mbox{\textit{OCR H240/02 2018 Q14 [7]}}