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.

A bag contains four tickets marked with numbers 112,121,211, and 222 . One ticket is drawn at random from the bag. Let E_(i)(i=1,2,3) denote the event that ith digit on the ticket is 2 . Then

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

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let x_i be the number on the card drawn from the ith box, i = 1, 2, 3. The probability that x_1, x_2, x_3 are in an aritmetic progression is

Box 1 contains three cards bearing numbers 1, 2,3, box 2 contains five cards bearing numbers 1,2,3,4,5, and box 3 contains seven card bearing numbers 1,2,3,4,5,6,7. Acard is drawn from each of the boxes. Let, x_(i) be the number on the card drawn from the i^(th) box i = 1,2,3. The probability that x_(1), x_(2), x_(3) are in an arithmetic progression, is-

A bag contains 50 tickets numbered 1, 2, 3, .., 50 of which five are drawn at random and arranged in ascending order of magnitude (x_1ltx_2ltx_3ltx_4ltx_5) find the probability that x_3=30 .

Let A and B be two events such that p( bar (AuuB))=1/6, p(AnnB)=1/4 and p( bar A)=1/4 , where bar A stands for the complement of the event A. Then the events A and B are (1) mutually exclusive and independent (2) equally likely but not independent (3) independent but not equally likely (4) independent and equally likely

Given that the events A and B are such that P(A) = (1)/(2), P(A cup B)=(3)/(5) and P(B) = p. Find p if they are (i) mutually exclusive (ii) independent.

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, 'the number is even,' and B be the event, 'the number is red'. Are A and B independent?

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, the number is even, and B be the event, the number is red. Are A and B independent?

Box 1 contains three cards bearing numbers 1, 2,3, box 2 contains five cards bearing numbers 1,2,3,4,5, and box 3 contains seven card bearing numbers 1,2,3,4,5,6,7. Acard is drawn from each of the boxes. Let, x_(i) be the number on the card drawn from the i^(th) box i = 1,2,3. The probability that x_(1) + x_(2), + x_(3) is odd,is-