Question

According to the general equation for conditional probability, if P(AB)=1/6

and P(B) = 7/18, what is P(AIB)?

Answer 1

`\sf P(A|B)= (3)/(7)`

Explanation:

The general equation for conditional probability is:

`\boxed{\begin{minipage}{5 cm}\underline{Conditional Probability formula}\\\\$\sf P(A|B)=(P(A \cap B))/(P(B))$\\\end{minipage}}`

Given probabilities:

`\sf P(A \cap B)=(1)/(6)`

`\sf P(B)=(7)/(18)`

Substitute the given probabilities into the equation and solve for P(A|B).

`\implies \sf P(A|B)= (1)/(6) / (7)/(18)`

`\implies \sf P(A|B)= (1)/(6) *(18)/(7)`

`\implies \sf P(A|B)= (18)/(42)`

Reduce the fraction to its simplest form by dividing the numerator and denominator by 6:

`\implies \sf P(A|B)= (3 \cdot \diagup\!\!\!\!6)/(7 \cdot \diagup\!\!\!\!6)`

`\implies \sf P(A|B)= (3)/(7)`