If C and D are two events such that \[C \subset D\] and \[P\left( D \right) \ne 0,\] then the correct statement among the following is :
Solutions · 1
Official solution
Given that \[C \subset D\] means C is present entirely inside D. Which is shown below.
\[P\left( {{C \over D}} \right)\] = \[{{P\left( {C \cap D} \right)} \over {P\left( D \right)}}\] = \[{{P\left( C \right)} \over {P\left( D \right)}}\]
As \[C \cap D\] means common part of events C and D which is equal to C.
\[0 \le P\left( D \right) \le 1\]
\[\therefore\] \[{{P\left( C \right)} \over {P\left( D \right)}} \ge P\left( C \right)\]
Note: Here we are dividing with \[{P\left( D \right)}\] which is \[ \le 1\] and \[ \ge 0\], as we know on dividing with a number n in the range \[0 \le n \le 1\] we get always more than or equal to the original number.