Q75 / 160 · AP EAMCET 2024 (21 May Shift 1) · Mathematics
If 12 dice are thrown at a time, then the probability that a multiple of 3 does not appear on any dice is
- A$\left(\frac{1}{2}\right)^{12}$
- B$\left(\frac{1}{3}\right)^{12}$
- Correct answerC$\left(\frac{2}{3}\right)^{12}$
- D$\left(\frac{5}{6}\right)^{12}$
Solution
Let A be the event that a multiple of 3 does not appear.
$\mathrm{P}(\mathrm{~A})=\frac{4}{6}=\frac{2}{3}$
Probability that a multiple of 3 does not appear on any $\text { dice }=\left(\frac{2}{3}\right)^{12}$
Probability that a multiple of 3 does not appear on any $\text { dice }=\left(\frac{2}{3}\right)^{12}$
Hence, the correct answer is option: 'C'.