For any two events `A_1` and `A_2`, prove that `P(A_1 nn A_2) le min{PA_1),P(A_2)}` where min`{PA_1),P(A_2)}` is the minimum of `P(A_1)` and `P(A_2)`.

For any two events A_1 and A_2 , show that P(A_1 cap A_2)lemin{P(A_1),P(A_2)} where min {P(A_1), P(A_2)} is the minimum of P(A_1) and P(A_2) .

Show that P(B)>0 , then P(A_1 cup A_2|B) = P(A_1|B) + P(A_2|B)-P(A_1 cap A_2|B) .

For three event A_1 , A_2 and A_3 state and prove Bonferroni's inequality.

Prove that, if A_1 and A_2 are two events, which are not necessarily mutually exclusive then P(A_1 uu A_2) = P(A_1) + P(A_1 nn A_2)

If A_1 , A_2 , A_3 are mutually exclusive and exhaustive, then P(A_1) + P(A_2) + P(A_3) equal______

If P(A_1) = 0.2 , P(A_2) = 0.1 and P(A_3) = 0.3 and these events are mutually independent, then what is the value of P(A_1 nn A_2 nn A_3) ?

Write the differences : Vitamin A_1 and Vitamin A_2

If the area of the circle is A_1 and the area of the regular pentagon inscribed in the circle is A_2, then find the ratio (A_1)/(A_2)dot

In each following cases, the amplitude of the first two oscillations A_1 and A_2 of a damped pendulum are given. What will be the amplitude of the pendulum in its third oscillation? (i) A_1=3.0 cm. A_2=2.4 cm (ii) A_1=5.0 cm, A_2=4.9 cm (iii) A_1=4.0 cm, A_2=2.0 cm

Let A_r ,r=1,2,3, , be the points on the number line such that O A_1,O A_2,O A_3dot are in G P , where O is the origin, and the common ratio of the G P be a positive proper fraction. Let M , be the middle point of the line segment A_r A_(r+1.) Then the value of sum_(r=1)^ooO M_r is equal to (a) (O A_1(O S A_1-O A_2))/(2(O A_1+O A_2)) (b) (O A_1(O A_2+O A_1))/(2(O A_1-O A_2) (c) (O A_1)/(2(O A_1-O A_2)) (d) oo