Question

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting equal numbers on the dice is

• A. 0.2
• B. 0.1
• C. 0.5
• D. 0.25

Answer 1

The correct option is A 0.2

$\mathrm{Let}\mathrm{us}\mathrm{define}\mathrm{the}\mathrm{events}A:‘\mathrm{getting}\mathrm{equal}\mathrm{numbers}\mathrm{on}\mathrm{dice}’.B:‘\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{numbers}\mathrm{is}\mathrm{less}\mathrm{than}6’.\mathrm{Then}\mathrm{we}\mathrm{have}\mathrm{to}\mathrm{find}P\left(A|B\right).\mathrm{Sample}\mathrm{space},S=\left(\left(x,y\right):x,y=1,2,3,4,5,6\right\}.\mathrm{Thus},n\left(S\right)=36A=\left(\left(1,1\right),\left(2,2\right),\left(3,3\right),\left(4,4\right),\left(5,5\right),\left(6,6\right)\right\}B=\left(\left(x,y\right):x+y<6\right\}i.e.,B=\left(\left(1,1\right),\left(1,2\right),\left(1,3\right),\left(1,4\right),\left(2,1\right),\left(2,2\right),\left(2,3\right),\left(3,1\right),\left(3,2\right),\left(4,1\right)\right\}i.e.,n\left(B\right)=10\mathrm{Clearly},A\cap B=\left(\left(1,1\right),\left(2,2\right)\right\}\mathrm{Now},P\left(B\right)=\frac{10}{36}\mathrm{and}P\left(A\cap B\right)=\frac{2}{36}\mathrm{Then}P\left(A|B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}\Rightarrow P\left(A|B\right)=\frac{\frac{2}{36}}{\frac{10}{36}}\Rightarrow P\left(A|B\right)=\frac{2}{10}=0.2$