Question

An engineering firm is hired to determine if certain waterways in Virginia are safe for fishing. Samples

are taken from three rivers.
(a) List the elements of a sample space S, using the letters F for safe to fish and N for not safe to fish.
(b) List the elements of S corresponding to event E that at least two of the rivers are safe for fishing.
(c) Define an event that has as its elements the points {FFF, NFF, FFN, NFN}

Answer 1

(a) S = {FFF, FFN, FNN, FNF, NNN, NNF, NFF, NFN}

(b) S(E) = {FFF, FFN, FNF, NFF}

(c) Second river is safe for fishing

Explanation:

F = safe to fish

N = not safe to fish

number of rivers sampled = 3

(a) All of the possible outcomes obtained from the samples are listed in the sample space bellow:

S = {FFF, FFN, FNN, FNF, NNN, NNF, NFF, NFN}

(b) If at least two rivers are safe, the sample space for E is all of the events with two or three safe rivers:

S(E) = {FFF, FFN, FNF, NFF}

(c) In the set {FFF, NFF, FFN, NFN}, the second lake sample is safe to fish in all of the elements. The event is: second river is safe for fishing.