Correct Answer - Option 2 :
\(\frac 1 3\)
Concept:
Conditional Probability: The probability of an event occurring given that another event has already occurred is called a conditional probability.
The probability of occurrence of any event A when another event B in relation to A has already occurred is known as conditional probability. It is depicted by P (A|B).
\({\rm{P}}\left( {{\rm{A}}|{\rm{B}}} \right) = \frac{{{\rm{P}}\left( {{\rm{A}} ∩ {\rm{B}}} \right)}}{{{\rm{P}}\left( {\rm{B}} \right)}}\)
Calculation:
Sample space is {1, 2, 3, 4, 5, 6}
Let A be the number obtained on dice is less than 4 and B is the number obtained on dice is even number.
A = {1, 2, 3} and B = {2, 4, 6}
P (A) = \(\frac 3 6\) and P (B) = \(\frac 3 6\)
Now, A ∩ B = {2}
P(A ∩ B) = \(\frac 1 6\)
Applying the conditional probability formula we get,
\({\rm{P}}\left( {{\rm{A}}|{\rm{B}}} \right) = \frac{{{\rm{P}}\left( {{\rm{A}} ∩ {\rm{B}}} \right)}}{{{\rm{P}}\left( {\rm{B}} \right)}} = \rm \frac{\frac{1}{6}}{\frac{3}{6}}=\frac{1}{3}\)
