Question Number 207751 by efronzo1 last updated on 25/May/24
![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 number 8. However, if an even number appears , the number is replaced with the number 1. Then the dice whose dice have been replaced are thrown again, the probability of an odd dice odd dice appearing is □ (1/3) □ (2/3) □ (1/2) □ 1](https://www.tinkutara.com/question/Q207751.png)
$$\:\:\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\mathrm{a}\:\mathrm{balanced}\:\mathrm{6}−\mathrm{sided}\: \\ $$$$\:\mathrm{dice}\:\mathrm{originally}\:\mathrm{had}\:\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\:\mathrm{and}\:\mathrm{7}. \\ $$$$\:\mathrm{The}\:\mathrm{dice}\:\mathrm{wre}\:\mathrm{thrown}\:\mathrm{once}\:\mathrm{and}\: \\ $$$$\:\mathrm{the}\:\mathrm{result}\:\mathrm{was}\:\mathrm{observed}.\:\mathrm{If}\:\mathrm{an}\: \\ $$$$\mathrm{odd}\:\mathrm{numbers}\:\mathrm{appears},\:\mathrm{than}\:\mathrm{the}\: \\ $$$$\:\mathrm{number}\:\mathrm{is}\:\mathrm{replaced}\:\mathrm{with}\:\mathrm{the}\: \\ $$$$\:\mathrm{number}\:\mathrm{8}.\:\mathrm{However},\:\mathrm{if}\:\mathrm{an}\:\mathrm{even}\: \\ $$$$\:\mathrm{number}\:\mathrm{appears}\:,\:\mathrm{the}\:\mathrm{number} \\ $$$$\:\mathrm{is}\:\mathrm{replaced}\:\mathrm{with}\:\mathrm{the}\:\mathrm{number}\:\mathrm{1}. \\ $$$$\:\mathrm{Then}\:\mathrm{the}\:\mathrm{dice}\:\mathrm{whose}\:\mathrm{dice}\:\mathrm{have}\: \\ $$$$\:\mathrm{been}\:\mathrm{replaced}\:\mathrm{are}\:\mathrm{thrown}\:\mathrm{again},\: \\ $$$$\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{dice}\: \\ $$$$\:\mathrm{odd}\:\mathrm{dice}\:\mathrm{appearing}\:\mathrm{is}\: \\ $$$$\:\:\Box\:\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\Box\:\frac{\mathrm{2}}{\mathrm{3}}\:\:\:\:\:\Box\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\Box\:\mathrm{1}\: \\ $$