TS EAMCET · Maths · Probability
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 \(P(\bigcap_{i=1}^{15} A_i) \geq \sum_{i=1}^{15} P\left(A_i\right)-14\)
- C \(P\left(\bigcup_{i=1}^{15} A_i\right) \geq \sum_{i=1}^{15} P\left(A_i\right)\)
- D \(P\left(\bigcup_{i=1}^{15} A_i\right) < \sum_{i=1}^{15} P\left(A_i\right)-\sum_{1 \leq i < j < 15} P\left(A_i \cap A_j\right)\)
Answer & Solution
Correct Answer
(B) \(P(\bigcap_{i=1}^{15} A_i) \geq \sum_{i=1}^{15} P\left(A_i\right)-14\)
Step-by-step Solution
Detailed explanation
(b) According to Booley's Inequalities. If \(A, B\) and \(C\) are the events of a random experiment that then \(P(A \cap B \cap C) \geq P(A)+P(B)+P(C)-2\) Similarly, If \(A_1, A_2, A_3, \ldots, A_{15}\) are the events of a random experiment, then…
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