Question

Consider an unbiased cubic dice with opposite faces coloured identically an each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is

• A. 0.2593

Answer 1

The correct option is A 0.2593

Let X = {No. of times red color on top face}

where p = P (red color) $=\frac{2}{6}$

q = P (other color) $=\frac{4}{6}$

n = 3

$P[X\ge 2]=P(X=2)+P(X=3)$

$={}^3{C}_2{\left(\frac{{}^2{C}_1}{{}^6{C}_1}\right)}^2\times \left(\frac{{}^4{C}_1}{{}^6{C}_1}\right)+{}^3{C}_3{\left(\frac{{}^2{C}_1}{{}^6{C}_1}\right)}^3$

$=3\times {\left(\frac{1}{3}\right)}^2\times \frac{2}{3}+1\times {\left(\frac{1}{3}\right)}^3$

$P=\frac{7}{27}=0.2593$