If $A_1, A_2, \ldots, A_{15}$ are the events of a random experiment, then which one of the following is true?

• A
  $P\left(\bigcap_{i=1}^{15} A_i\right) \leq \sum_{i=1}^{15} P\left(A_i\right)-15$
• B
  $P\left(\bigcap_{i=1}^{15} A_i\right) \geq \sum_{i=1}^{15} P\left(A_i\right)-14$
• C
  $P\left(\bigcup_{i=1}^{15} A_i\right) \geq \sum_{i=1}^{15} P\left(A_i\right)$
• D
  $P\left(\bigcup_{i=1}^{15} A_i\right) < \sum_{i=1}^{15} P\left(A_i\right)-\sum_{1 \leq i < j \leq 15} P\left(A_i \cap A_j\right)$