Let omega be a complex cube root of unity wit | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$ \mathrm{r}_1, \mathrm{r}_2, \mathrm{r}_3 \in\{1,2,3,4,5,6\} $

$ \mathrm{r}_1, \mathrm{r}_2, \mathrm{r}_3 	ext { are of the form } 3 \mathrm{k},

Vedclass · Accepted Answer

$\frac{2}{9}$

Vedclass · Answer

$ \mathrm{r}_1, \mathrm{r}_2, \mathrm{r}_3 \in\{1,2,3,4,5,6\} $

$ \mathrm{r}_1, \mathrm{r}_2, \mathrm{r}_3 	ext { are of the form } 3 \mathrm{k}, 3 \mathrm{k}+1,3 \mathrm{k}+2 $

$ 	ext { Required probability }=\frac{3!	imes{ }^2 \mathrm{C}_1 	imes{ }^2 \mathrm{C}_1 	imes{ }^2 \mathrm{C}_1}{6 	imes 6 	imes 6}=\frac{6 	imes 8}{216}=\frac{2}{9}$

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 $\omega^{I_1}+\omega^{\mathrm{I}_2}+\omega^{\mathrm{I}_3}=0$ is

Similar Questions

Among $15$ players, $8$ are batsmen and $7$ are bowlers. Find the probability that a team is chosen of $6$ batsmen and $5$ bowlers

If $7$ dice are thrown simultaneously, then probability that all six digit appears on the upper face is equal to -

A bag has $13$ red, $14$ green and $15$ black balls. The probability of getting exactly $2$ blacks on pulling out $4$ balls is ${P_1}$. Now the number of each colour ball is doubled and $8$ balls are pulled out. The probability of getting exactly $4$ blacks is ${P_2}.$ Then

In a certain lottery $10,000$ tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy two ticket.

A cricket team has $15$ members, of whom only $5$ can bowl. If the names of the $15$ members are put into a hat and $11$ drawn at random, then the chance of obtaining an eleven containing at least $3$ bowlers is