It-is-known-that-a-balanced-6-sided-dice-originally-had-2-3-4-5-6-and-7-The-dice-wre-thrown-once-and-the-result-was-observed-If-an-odd-numbers-appears-than-the-number-is-replaced-with-the

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Question Number 207751 by efronzo1 last updated on 25/May/24

$$\mathrm{It}\mathrm{is}\mathrm{known}\mathrm{that}\mathrm{a}\mathrm{balanced}6-\mathrm{sided}$$$$\mathrm{dice}\mathrm{originally}\mathrm{had}2,3,4,5,6\mathrm{and}7.$$$$\mathrm{The}\mathrm{dice}\mathrm{wre}\mathrm{thrown}\mathrm{once}\mathrm{and}$$$$\mathrm{the}\mathrm{result}\mathrm{was}\mathrm{observed}.\mathrm{If}\mathrm{an}$$$$\mathrm{odd}\mathrm{numbers}\mathrm{appears},\mathrm{than}\mathrm{the}$$$$\mathrm{number}\mathrm{is}\mathrm{replaced}\mathrm{with}\mathrm{the}$$$$\mathrm{number}8.\mathrm{However},\mathrm{if}\mathrm{an}\mathrm{even}$$$$\mathrm{number}\mathrm{appears},\mathrm{the}\mathrm{number}$$$$\mathrm{is}\mathrm{replaced}\mathrm{with}\mathrm{the}\mathrm{number}1.$$$$\mathrm{Then}\mathrm{the}\mathrm{dice}\mathrm{whose}\mathrm{dice}\mathrm{have}$$$$\mathrm{been}\mathrm{replaced}\mathrm{are}\mathrm{thrown}\mathrm{again},$$$$\mathrm{the}\mathrm{probability}\mathrm{of}\mathrm{an}\mathrm{odd}\mathrm{dice}$$$$\mathrm{odd}\mathrm{dice}\mathrm{appearing}\mathrm{is}$$$$\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.0.3/svg/25fb.svg">}\frac{1}{3}\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.0.3/svg/25fb.svg">}\frac{2}{3}\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.0.3/svg/25fb.svg">}\frac{1}{2}\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.0.3/svg/25fb.svg">}1$$

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