Addition Theorem of Events MCQ Quiz in मराठी - Objective Question with Answer for Addition Theorem of Events - मोफत PDF डाउनलोड करा

Last updated on Apr 11, 2025

पाईये Addition Theorem of Events उत्तरे आणि तपशीलवार उपायांसह एकाधिक निवड प्रश्न (MCQ क्विझ). हे मोफत डाउनलोड करा Addition Theorem of Events एमसीक्यू क्विझ पीडीएफ आणि बँकिंग, एसएससी, रेल्वे, यूपीएससी, स्टेट पीएससी यासारख्या तुमच्या आगामी परीक्षांची तयारी करा.

Latest Addition Theorem of Events MCQ Objective Questions

Top Addition Theorem of Events MCQ Objective Questions

Addition Theorem of Events Question 1:

Let A and B are two independent events. The probability that both A and B happen is 112 and probability that neither A nor B happen is 12 Then

  1. P(A)=13,P(B)=14
  2. P(A)=12,P(B)=16
  3. P(A)=16,P(B)=12
  4. P(A)=23,P(B)=18

Answer (Detailed Solution Below)

Option 1 : P(A)=13,P(B)=14

Addition Theorem of Events Question 1 Detailed Solution

Calculation

P(A∩B) = 112 ⇒ P(A)P(B) = 112 ...(1)

P(A'∩B') = 12 ⇒ P(A∪B) = 1 - 12 = 12

⇒ P(A) + P(B) - P(A)P(B) = 12

⇒ P(A) + P(B) = 12 + 112 = 712

From (1),

P(A)(712 - P(A)) = 112

⇒ P(A)² - (712)P(A) + 112 = 0

⇒ 12P(A)² - 7P(A) + 1 = 0

⇒ 12P(A)² - 4P(A) - 3P(A) + 1 = 0

⇒ (3P(A) - 1)(4P(A) - 1) = 0

∴ P(A) = 13 or P(A) = 14

P(B) = 112 × 3 ⇒ P(B) = 14

P(B) = 112 × 4 ⇒ P(B) = 13

∴ P(A) = 13, P(B) = 14

Hence option 1 is correct

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