I don't get it why the Second Borel Cantelli Lemma here will get me to this conclusion, I don't see the link

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$Let\:\left(d_1\left(w\right),...\right)\:be\:a\:sequence\:for\:which\:d_{n\:}\left(w\right)=1\:obverse\:and\:d_n\left(w\right)=0\:reverse,\:let\:A_n=\left\{d_n\left(w\right)=1\right\},\:P\left(A_n\right)=\frac{1}{2}.\:Why,\:according\:to\:second\:Borel-Cantelli\:Lemma,\:the\:probability\:for\:\infty \:many\:occurring\:1\:is\:equal\:to\:100\%?$