jee-advanced 2010 Q31

jee-advanced · India · paper1 Conditional Probability Combinatorial Conditional Probability (Counting-Based)

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. A fair die is thrown three times. If $r _ { 1 } , r _ { 2 }$ and $r _ { 3 }$ are the numbers obtained on the die, then the probability that $\omega ^ { r _ { 1 } } + \omega ^ { r _ { 2 } } + \omega ^ { r _ { 3 } } = 0$ is
A) $\frac { 1 } { 18 }$
B) $\frac { 1 } { 9 }$
C) $\frac { 2 } { 9 }$
D) $\frac { 1 } { 36 }$

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. A fair die is thrown three times. If $r _ { 1 } , r _ { 2 }$ and $r _ { 3 }$ are the numbers obtained on the die, then the probability that $\omega ^ { r _ { 1 } } + \omega ^ { r _ { 2 } } + \omega ^ { r _ { 3 } } = 0$ is\\
A) $\frac { 1 } { 18 }$\\
B) $\frac { 1 } { 9 }$\\
C) $\frac { 2 } { 9 }$\\
D) $\frac { 1 } { 36 }$

Paper Questions

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