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Q.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 , the probability of getting a sum 3 , is
Probability - Part 2
Solution:
When two dice are thrown, then the number of events in the sample space $=36$
Let $A$ : sum of the numbers on the dice was less than 6 and $B$ : getting a sum equals to 3 .
Then, $A=\{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3).(3,1),(3,2),(4,1)\}$
$B=\{(1,2),(2,1)\}$
and $ A \cap B=\{(1,2),(2,1)\}$
$\therefore P(A \cap B)=\frac{2}{36}=\frac{1}{18}$
$P(A)=\frac{10}{36}=\frac{5}{18}$
Now, $P\left(\frac{B}{A}\right)=\frac{P(A \cap B)}{P(A)}=\frac{\frac{1}{18}}{\frac{5}{18}}=\frac{1}{5}$