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Roll-a-fair-die-twice-and-define-A-to-be-event-that-the-sum-of-the-scores-showing-up-is-greater-than-7-B-be-the-event-that-the-sum-of-the-scores-showing-up-is-a-multiple-of-3-and-C-be-the-event-that-




Question Number 150030 by jlewis last updated on 08/Aug/21
Roll a fair die twice and define A to be  event that the sum of the scores showing  up is greater than 7, B be the event that  the sum of the scores showing up is a  multiple of 3 and C be the event that   the sum of the scores showing up is a  prime number. Which of the events   A,B and C are independent event?  are the 3 events jointly independent?
$$\mathrm{Roll}\:\mathrm{a}\:\mathrm{fair}\:\mathrm{die}\:\mathrm{twice}\:\mathrm{and}\:\mathrm{define}\:\mathrm{A}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{event}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing} \\ $$$$\mathrm{up}\:\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{7},\:\mathrm{B}\:\mathrm{be}\:\mathrm{the}\:\mathrm{event}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing}\:\mathrm{up}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}\:\mathrm{and}\:\mathrm{C}\:\mathrm{be}\:\mathrm{the}\:\mathrm{event}\:\mathrm{that} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing}\:\mathrm{up}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{prime}\:\mathrm{number}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{events}\: \\ $$$$\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{independent}\:\mathrm{event}? \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{3}\:\mathrm{events}\:\mathrm{jointly}\:\mathrm{independent}? \\ $$$$ \\ $$

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