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Question-66683




Question Number 66683 by Tinkutara@ last updated on 18/Aug/19
Commented by mr W last updated on 18/Aug/19
each runner has two possibilities, totally  2×2×2=8. such that they don′t collide,  all of them must run in the same  direction, there are two such possibilities.  the probability that they don′t collide  is therefore (2/(2×2×2)), and that that  they collide is 1−(2/(2×2×2))=1−(1/4)=(3/4)  =0.75
$${each}\:{runner}\:{has}\:{two}\:{possibilities},\:{totally} \\ $$$$\mathrm{2}×\mathrm{2}×\mathrm{2}=\mathrm{8}.\:{such}\:{that}\:{they}\:{don}'{t}\:{collide}, \\ $$$${all}\:{of}\:{them}\:{must}\:{run}\:{in}\:{the}\:{same} \\ $$$${direction},\:{there}\:{are}\:{two}\:{such}\:{possibilities}. \\ $$$${the}\:{probability}\:{that}\:{they}\:{don}'{t}\:{collide} \\ $$$${is}\:{therefore}\:\frac{\mathrm{2}}{\mathrm{2}×\mathrm{2}×\mathrm{2}},\:{and}\:{that}\:{that} \\ $$$${they}\:{collide}\:{is}\:\mathrm{1}−\frac{\mathrm{2}}{\mathrm{2}×\mathrm{2}×\mathrm{2}}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$=\mathrm{0}.\mathrm{75} \\ $$
Commented by Tinkutara@ last updated on 18/Aug/19
thanks sir!
$${thanks}\:{sir}! \\ $$
Answered by JDamian last updated on 18/Aug/19
0.75
$$\mathrm{0}.\mathrm{75} \\ $$

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