Verified Solution • 2025–26 Session moderate

QJEEM23Mafd43: JEE Main 2023 Mathematics - Class 12 JEEM23Mafd43 Solution: If an unbiased die, marked with on its faces, is thrown five…

If an unbiased die, marked with −2,−1,0,1,2,3-2,-1,0,1,2,3 on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is :

Multiple Choice Options

  • A 27288\frac{27}{288}
  • B 5212592\frac{521}{2592}
  • C 4402592\frac{440}{2592}
  • D 8812592\frac{881}{2592}

Step-by-Step Verified Solution

5C0×35=243{}^5{C_0} \times {3^5} = 243

5C2×22×33=1080{}^5{C_2} \times {2^2} \times {3^3} = 1080

5C4×24 . 3=240{}^5{C_4} \times {2^4}\,.\,3 = 240

∴\therefore required probability

=243+1080+2406×6×6×6×6=5212592= {{243 + 1080 + 240} \over {6 \times 6 \times 6 \times 6 \times 6}} = {{521} \over {2592}}

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