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.
(i) Calculate the probability that they will catch fewer than 2 fish in total on a randomly selected half-day of fishing.
(ii) Justify any distribution you have used in answering (a)(i).
On a randomly selected day, Dave starts fishing at 7 am. Given that Dave has not caught a fish by 11 am,
find the expected time he catches his first fish,
calculate the probability that he will not catch a fish by 3 pm .
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]
State, with a reason, a distribution, including any parameters, that could approximate the distribution used in part (c).