AP EAMCET20224 Jul 2022Evening ShiftMathematicsProbabilityActual

For two events A and B , a true statement among the following is

Options

AP A ¯ ∪ B ¯ = 1 - P A P B A
BP A ¯ ∪ B ¯ = 1 - P A ∪ B
CP A ¯ ∪ B ¯ = P A ∪ B
DP A ¯ ∪ B ¯ = P A ¯ + P B ¯

Correct answer

A. P A ¯ ∪ B ¯ = 1 - P A P B A

Step-by-step solution

We know that P B A = P A ∩ B P A ⇒ P A P B A = P A ∩ B   . . . . . . . 1 Now solving option A we get, P A ¯ ∪ B ¯ = P A ∩ B ¯ by demorgan's law ⇒ P A ¯ ∪ B ¯ = 1 - P A ∩ B ⇒ P A ¯ ∪ B ¯ = 1 - P A P B A

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