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Let A and B be two events such that P B ∣ A = 2 5 , P A ∣ B = 1 7 and P A ∩ B = 1 9 . Consider S 1 P A ' ∪ B = 5 6 , S 2 P A ' ∩ B ' = 1 18 . Then

Options

  1. ABoth S 1 and S 2 are true
  2. BBoth S 1 and S 2 are false
  3. COnly S 1 is true
  4. DOnly S 2 is true

Correct answer

A. Both S 1 and S 2 are true

Step-by-step solution

Given, A and B be two events such that P B ∣ A = 2 5 , P A ∣ B = 1 7 and P A ∩ B = 1 9 , Now using the formula of conditional probability we get, P A ∣ B = 1 7 ⇒ P A ∩ B P B = 1 7 ⇒ 1 9 P B = 1 7 ⇒ P B = 7 9 Now again using formula we get, P B ∣ A = 2 5 ⇒ P A ∩ B P A = 2 5 ⇒ 1 9 P A = 2 5 ⇒ P A = 5 18 Now we know that, P A ' ∪ B = 1 - P A ∪ B + P B ⇒ P A ' ∪ B = 1 - P A + P A ∩ B = 5 6 And P A ' &

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