যে কোন দুটি স্বাধীন ঘটনা A এবং B, P(A - B) এর সমান:

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SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )
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  1. P(A) - P(A)P(B)
  2. P(B)- P(A)
  3. P(B) (1 - P(AB))
  4. P(A) - P(B)

Answer (Detailed Solution Below)

Option 1 : P(A) - P(A)P(B)
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Detailed Solution

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প্রদত্ত:

দুটি স্বাধীন ঘটনা A এবং B

অনুসৃত সূত্র:

P(A - B) = P(A) - P(A ∩ B)

স্বাধীন ঘটনার জন্য, P(A ∩ B) = P(A) × P(B)

গণনা:

আমাদের P(A - B) নির্ণয় করতে হবে।

P(A - B) = P(A) - P(A ∩ B)

যেহেতু A এবং B স্বাধীন ঘটনা:

P(A ∩ B) = P(A) × P(B)

অতএব, P(A - B) = P(A) - P(A) × P(B)

সমাধান:

P(A - B) = P(A) - P(A) × P(B)

P(A - B) = P(A)(1 - P(B))

সুতরাং, P(A - B) = P(A)(1 - P(B))

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