Moderate -0.8 Part (a) requires setting up a basic probability equation P(success) = p + (1-p)p = 0.64 and solving a simple quadratic, which is routine AS-level work. Part (b) is straightforward conditional probability with small numbers requiring no complex reasoning. Both parts are standard textbook exercises with no novel insight required, making this easier than average.
Marie is an athlete who competes in the high jump. In a certain competition she is allowed two attempts to clear each height, but if she is successful with the first attempt she does not jump again at this height. The probability that she is successful with her first jump at a height of \(1 \cdot 7\) m is \(p\). The probability that she is successful with her second jump is also \(p\). The probability that she clears \(1 \cdot 7\) m is \(0 \cdot 64\). Find the value of \(p\). [4]
The following table shows the numbers of male and female athletes competing for Wales in track and field events at a competition.
Track
Field
Male
13
9
Female
7
4
Two athletes are chosen at random to participate in a drugs test. Given that the first athlete is male, find the probability that both are field athletes. [3]
\begin{enumerate}[label=(\alph*)]
\item Marie is an athlete who competes in the high jump. In a certain competition she is allowed two attempts to clear each height, but if she is successful with the first attempt she does not jump again at this height. The probability that she is successful with her first jump at a height of $1 \cdot 7$ m is $p$. The probability that she is successful with her second jump is also $p$. The probability that she clears $1 \cdot 7$ m is $0 \cdot 64$. Find the value of $p$. [4]
\item The following table shows the numbers of male and female athletes competing for Wales in track and field events at a competition.
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
& Track & Field \\
\hline
Male & 13 & 9 \\
\hline
Female & 7 & 4 \\
\hline
\end{tabular}
\end{center}
Two athletes are chosen at random to participate in a drugs test. Given that the first athlete is male, find the probability that both are field athletes. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 4 2018 Q2 [7]}}