Maths Statistics QuestionWatch this thread
Players use a hook on the end of a piece of string to catch a plastic duck floating in a pool.
Each duck looks the same but has a number written on the bottom; 1, 2, 3 or 4
There are 20 ducks in the pool, 5 with each number.
(a) State the distribution which may be used to model the number on a duck hooked by a randomly selected player.
Calculate the probability that of the first 3 ducks hooked,
(b) all 3 have the same number,
(c) exactly 2 of them have the same number.
During the day 200 ducks are hooked.
The random variable X is defined as the number of ducks out of 200 that have an even number.
(d) State an appropriate distribution which may be used to model the random Variable X.
(e) State a necessary assumption about hooking the ducks which must be true for this distribution to be a good model.
(f) Use this model to calculate the probability that, out of the 200 ducks hooked that day, at least 110 ducks have even numbers.
Jaime suggests using a normal approximation to estimate P(X>=110)
(g)State, giving a reason, whether or not this suggestion is reasonable.
(h) Calculate the error in using Jaime's suggestion
You should show your work clearly and give your answer to 2 significant figures.
Any ideas on a)?
For b), let's suppose the first duck hooked is 1 (it could be something else). What is p(second duck = 1)? What is p(third duck = 1)?
Try this to begin then that will help with the other parts.