Question

Three faces of an ordinary dice are yellow, two faces are red and one face is blue. The dice is tossed $3$ times. The probability that yellow, red and blue faces appear in the first, second and third tosses respectively is

• A. $\frac{1}{36}$
• B. $\frac{1}{6}$
• C. $\frac{1}{30}$
• D. none of these

Answer 1

The correct option is A $\frac{1}{36}$

Let's represent yellow face by Y,Red face by R and blue face by B.
$P\left(Y\right)=\frac{3}{6}=\frac{1}{2}P\left(R\right)=\frac{2}{6}=\frac{1}{3}P\left(B\right)=\frac{1}{6}$
Let's call YRB to be the desired event
Then $P\left(YRB\right)=P\left(Y\right)\times P\left(R\right)\times P\left(B\right)\Rightarrow P\left(YRB\right)=\frac{1}{2}\times \frac{1}{3}\times \frac{1}{6}=\frac{1}{36}$