Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Probability Inequalities
Let E and F be two events in a discrete probability space. Assume that ℙ(E) > 0, ℙ(F) > 0 and that E and F are independent. Which of the following statements are necessarily true?
1
ℙ(E ∩ F) = ℙ(E) x ℙ(F)
2
ℙ(E ∪ F) = ℙ(E) + ℙ(F) - ℙ(E) x ℙ(F)
3
If ℙ(E | F) > ℙ(E), then F and E are dependent.
4
If ℙ(E | F) = ℙ(E), then E and F are dependent.