Let A and E be any two events with positive probabilities Statement I: P E / A ≥ P A / E P E . Statement II: P A / E ≥ P A ∩ E .

Question

Let A and E be any two events with positive probabilities Statement I: P E / A ≥ P A / E P E . Statement II: P A / E ≥ P A ∩ E ., Both the statements are false, Both the statements are true, Statement - I is false, Statement - II is true, Statement - I is true, Statement - II is false

MARKS App · Accepted Answer

We know that P E / A = P E ∩ A P A ⇒ P E ∩ A = P E / A · P A . . . i Also, P A / E = P E ∩ A P E ⇒ P E ∩ A = P A / E · P E i i From the equations i and i i , we get P E / A · P A = P A / E · P E Now, since 0 P A ≤ 1 ⇒ P E / A ≥ P A / E · P E Again, we have P A / E = P E ∩ A P E ⇒ P A / E · P E = P E ∩ A Now, since 0 P E ≤ 1 P A / E ≥ P A ∩ E ⇒ Both the statements are true.

Search any question & find its solution

Looking for more such questions to practice?