Question

Three faces of a fair die are yellow, two faces red and one blue. The die is tossed three times. The probability that the colours yellow, red and blue, appear in the first, second and the third tosses respectively is $1/k$, then find $\sqrt{k}$.

Answer 1

Probability(Yellow appears) $=P\left(Y\right)=\frac{3}{6}=\frac{1}{2}$
Probability(Red appears) $=P\left(R\right)=\frac{2}{6}=\frac{1}{3}$
Probability(Blue appears) $=P\left(B\right)=\frac{1}{6}$
Since there are mutually exclusive and independent events.
Probability(Yellow is first, red is second and blue is third)
$=P\left(Y\right).P\left(R\right).P\left(B\right)=\frac{1}{2}.\frac{1}{3}.\frac{1}{6}=\frac{1}{36}$
$\therefore k=6$