Question

Mark the correct alternative in the following question:

Two dice are thrown. If it is known that the sum of the numbers on the dice was less than 6, then the probability of getting a sum 3, is

$\left(\mathrm{a}\right)\frac{1}{18}\left(\mathrm{b}\right)\frac{5}{18}\left(\mathrm{c}\right)\frac{1}{5}\left(\mathrm{d}\right)\frac{2}{5}$

Answer 1

$$\begin{gathered} \mathrm{Let}: \\ A\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{sum}\mathrm{of}3\mathrm{and} \\ B\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{sum}\mathrm{of}6 \\ \mathrm{As},A=\left\{\left(1,2\right),\left(2,1\right)\right\}\mathrm{and}B=\left\{\left(1,1\right),\left(1,2\right),\left(1,3\right),\left(1,4\right),\left(2,1\right),\left(2,2\right),\left(2,3\right),\left(3,1\right),\left(3,2\right),\left(4,1\right)\right\} \\ \mathrm{So},\mathrm{n}\left(A\right)=2,\mathrm{n}\left(\mathit{B}\right)=10\mathrm{and}\mathrm{n}\left(A\cap B\right)=\mathrm{n}\left(A\right)=2 \\ \mathrm{Now}, \\ \mathrm{P}\left(A|B\right)=\frac{\mathrm{n}\left(A\cap B\right)}{\mathrm{n}\left(B\right)} \\ =\frac{2}{10} \\ =\frac{1}{5} \end{gathered}$$

Hence, the correct alternative is option (c).