Dave and Llinos like to go fishing. When they go fishing, on average, Dave catches 4.3 fish per day and Llinos catches 3.8 fish per day. A day of fishing is assumed to be 8 hours.\\
(a)
\begin{enumerate}[label=(\roman*)]
\item Calculate the probability that they will catch fewer than 2 fish in total on a randomly selected half-day of fishing.
\item Justify any distribution you have used in answering (a)(i).\\
\end{enumerate}(b) On a randomly selected day, Dave starts fishing at 7 am. Given that Dave has not caught a fish by 11 am,\\
\begin{enumerate}[label=(\roman*)]
\item find the expected time he catches his first fish,
\item calculate the probability that he will not catch a fish by 3 pm .\\
\end{enumerate}(c) On average, only $2 \%$ of the fish that Llinos catches are trout. Over the course of a year, she catches 950 fish. Calculate the probability that at least 30 of these fish are trout. [3]\\[0pt]
she catches 950 fish. Calculate the probability that at least 30 of these fish are trout. [3]\\

(d) State, with a reason, a distribution, including any parameters, that could approximate the distribution used in part (c).\\



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\hfill \mbox{\textit{WJEC Further Unit 2 2024 Q1 [14]}}