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

An urn contains 4 tickets having the nos. 112, 121, 211, 222. A ticket is drawn at random. The even A_i = the event that the i^(th) digit is 1 (I = 1 to 3). Shwo that the events A_1 , A_2 , A_3 are pair wise independent but not mutually independent.

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

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

Find the number of ways of arranging 15 students A_1,A_2,........A_15 in a row such that (i) A_2 , must be seated after A_1 and A_3 , must come after A_2 (ii) neither A_2 nor A_3 seated brfore A_1

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)

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) .

Write the differences : Vitamin A_1 and Vitamin A_2

If the coefficients of four consecutive terms in the expansion of (1+x)^n are a_1,a_2,a_3 and a_4 respectively. then prove that a_1/(a_1+a_2)+a_3/(a_3+a_4)=2a_2/(a_2+a_3).

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) ?

If a_1,a_2,a_3(a_1 gt0) are in G.P with common ratio r, then the value of r , for which the inequality 9 a_1+5a_3le14a_2 holds, can not lie in the interval.