Let A and B be two non-null events such that A [ ] B .

Question

Let A and B be two non-null events such that
A $$ \subset $$ B . Then, which of the following statements
is always correct?

Accepted Answer

$$P\left( {{A \over B}} \right) = {{P\left( {A \cap B} \right)} \over {P\left( B \right)}}$$

As A $$ \subset $$ B,

then P(A$$ \cap $$B) = P(A)

$$ \therefore $$ $$P\left( {{A \over B}} \right) = {{P\left( A \right)} \over {P\left( B \right)}}$$

As P(B) $$ \le $$ 1

$$ \therefore $$ $${{P\left( A \right)} \over {P\left( B \right)}}$$ $$ \ge $$ P(A)

Solutions · 1