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Sagot :
given:
[tex] \frac{1}{3} [/tex]
to find:
the probability of the coin.
solution:
lie:
[tex]( \frac{1}{3} ) \times ( \frac{1}{3}) \times ( \frac{1}{3} )[/tex]
[tex] = \frac{1}{27} [/tex]
there's 1/27 chance of them to lie.
truth:
[tex]( \frac{2}{3} ) \times ( \frac{2}{3} ) \times ( \frac{2}{3} )[/tex]
[tex] = \frac{8}{27} [/tex]
there's 8/27 chance that all of them told the truth.
probability:
[tex]( \frac{8}{27} ) \div (( \frac{8}{27} ) + ( \frac{1}{27} ))[/tex]
[tex] = \frac{8}{9} [/tex]
therefore, between those two chances, it's an 8/9 chance it's actually Heads.
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