Question

Rajnikant has $12$ sketch pens and $8$ fountain pens. He gave two of the pens to his brother. Find the probabilities of the following events using tree diagram :
i) Both the pens are sketch pens.
ii) Only one is a sketch pen.
iii) Neither of them are sketch pens.

Answer 1

i) $P=\frac{{}^{12}{C}_2}{{}^{20}{C}_2}=\frac{12\times 11}{20\times 19}=\frac{132}{380}=\frac{33}{95}$ (Image 1)

ii) $P=\frac{{}^{12}{C}_1{.}^8{C}_1}{{}^{20}{C}_2}=\frac{12\times 8\times 2}{20\times 19}=\frac{192}{380}=\frac{48}{95}$ (Image 2)

iii) $P=\frac{{}^{12}{C}_0{.}^8{C}_2}{{}^{20}{C}_2}=\frac{8\times 7}{20\times 19}=\frac{56}{380}=\frac{14}{95}$ (Image 3)