JEE Main2014MathematicsProbabilityActual
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 .
Options
- ABoth the statements are false
- BBoth the statements are true
- CStatement - I is false, Statement - II is true
- DStatement - I is true, Statement - II is false
Correct answer
B. Both the statements are true
Step-by-step solution
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 &#