As $\sum \limits_{ k =1}^{\infty} P \left( w _{ k }\right)=1 \Rightarrow \frac{\lambda}{1-\frac{1}{2}}=1 \Rightarrow \lambda=\frac{1}{2}$
So, $P \left( w _{ n }\right)=\frac{1}{2^{ n }}$
$A =\{2 k +3 \ell ; k , \ell \in N \}=\{5,7,8,9,10 \ldots .\}$
$B =\left\{ w _{ n }: n \in A \right\}$
$B =\left\{ w _5, w _7, w _8, w _9, w _{10}, w _{11}, \ldots .\right\}$
$A = N -\{1,2,3,4,6\}$
$\therefore P ( B )=1-\left[ P \left( w _1\right)+ P \left( w _2\right)+ P \left( w _3\right)+ P \left( w _4\right)+ P \left( w _6\right)\right]$
$=1-\left[\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{64}\right]$
$=1-\frac{32+16+8+4+1}{64}=\frac{3}{64}$
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