"Let $\mathrm{S} = \{ {w_1},{w_2},......\}$ be the sample space associated to a random experiment. Let $P({w_n}) = {{P({w_{n - 1}})} \over 2},n \ge 2$. Let $A = \{ 2k + 3l:k,l \in N\}$ and $B = \{ {w_n}:n \in A\}$. Then P(B) is equal to :"

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Accepted Answer

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$P({w_1}) + {{P({w_1})} \over 2} + {{P({w_1})} \over {{2^2}}}\, + \,..... = 1$

$\therefore$ $P({w_1}) = {1 \over 2}$

Hence, $P({w_n}) = {1 \over {{2^n}}}$

Every number except 1, 2, 3, 4, 6 is representable in the form

$2k + 3l$ where $k,l \in N$.

$\therefore$ $P(B) = 1 - P({w_1}) - P({w_2}) - P({w_3}) - P({w_4}) - P({w_6})$

$= {3 \over {64}}$

"

Let $\mathrm{S} = \{ {w_1},{w_2},......\}$ be the sample space associated to a random experiment. Let $P({w_n}) = {{P({w_{n - 1}})} \over 2},n \ge 2$. Let $A = \{ 2k + 3l:k,l \in N\}$ and $B = \{ {w_n}:n \in A\}$. Then P(B) is equal to :

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Let $\mathrm{S} = \{ {w_1},{w_2},......\}$ be the sample space associated to a random experiment. Let $P({w_n}) = {{P({w_{n - 1}})} \over 2},n \ge 2$. Let $A = \{ 2k + 3l:k,l \in N\}$ and $B = \{ {w_n}:n \in A\}$. Then P(B) is equal to :

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