If 12 dice are thrown at a time, then the probability that a multiple of 3 does not appear on any dice is

If 12 dice are thrown at a time, then the probability that a multiple of 3 does not appear on any dice is
  1. $\left(\frac{1}{2}\right)^{12}$
  2. $\left(\frac{1}{3}\right)^{12}$
  3. $\left(\frac{2}{3}\right)^{12}$
  4. $\left(\frac{5}{6}\right)^{12}$

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 $\text { dice }=\left(\frac{2}{3}\right)^{12}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

Practice more Probability questions on Aicharya