Verified Solution • 2025–26 Session moderate

QJEEM23Mad445: JEE Main 2023 Mathematics - Class 12 JEEM23Mad445 Solution: Let be the sample space associated to a random experiment. Let…

Let S={w1,w2,......}\mathrm{S} = \{ {w_1},{w_2},......\} be the sample space associated to a random experiment. Let P(wn)=P(wn−1)2,n≥2P({w_n}) = {{P({w_{n - 1}})} \over 2},n \ge 2 . Let A={2k+3l:k,l∈N}A = \{ 2k + 3l:k,l \in N\} and B={wn:n∈A}B = \{ {w_n}:n \in A\} . Then P(B) is equal to :

Multiple Choice Options

  • A 332\frac{3}{32}
  • B 132\frac{1}{32}
  • C 116\frac{1}{16}
  • D 364\frac{3}{64}

Step-by-Step Verified Solution

P(w1)+P(w1)2+P(w1)22 + .....=1P({w_1}) + {{P({w_1})} \over 2} + {{P({w_1})} \over {{2^2}}}\, + \,..... = 1

∴\therefore P(w1)=12P({w_1}) = {1 \over 2}

Hence, P(wn)=12nP({w_n}) = {1 \over {{2^n}}}

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

2k+3l2k + 3l where k,l∈Nk,l \in N .

∴\therefore P(B)=1−P(w1)−P(w2)−P(w3)−P(w4)−P(w6)P(B) = 1 - P({w_1}) - P({w_2}) - P({w_3}) - P({w_4}) - P({w_6})

=364= {3 \over {64}}

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