TS EAMCET · Maths · Probability
Consider the following statements Assertion (A) If \(P_1, P_2, P_3\) are probability of happening of three independent events, then probability of happening of atleast one of them is \(1-\left[\left(1-P_1\right)\left(1-P_2\right)\left(1-P_3\right)\right]\) Reason (R) For any three independent events \(A, B\) and \(C\) \(\begin{array}{r} P(A \cup B \cup C)=P(A)+P(B)+P(C)-P(A) P(B) \ -P(A) P(C)-P(B) P(C)+P(A) P(B) P(C) \end{array}\) The correct option among the following is
- A (A) is true, (R) is true and (R) is the correct explanation for (A)
- B (A) is true, (R) is true but (R) is not the correct explanation for (A)
- C (A) is true but (R) is false
- D (A) is false but (R) is true
Answer & Solution
Correct Answer
(A) (A) is true, (R) is true and (R) is the correct explanation for (A)
Step-by-step Solution
Detailed explanation
\(P_1, P_2, P_3\) are three independent events Probability of happening at least one event is \(1-\left[\left(\bar{P}_1\right) \cdot\left(\bar{P}_2\right)\left(\bar{P}_3\right)\right]=1-\left(1-\bar{P}_1\right)\left(1-\bar{P}_2\right)\left(1-\bar{P}_3\right)\) \(\therefore A\)…
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