Two dice are rolled simultaneously and counts are added (i) complete the table given
(ii) A student that 'there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefor, each of the them has a probability `1/11`. Do you agree with this argument? Justify your answer.

Which of the following arguments are correct and which are not correct? Give reasons. i) If two coins are tossed simultaneously there are three possible outcomes - two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3 ii)If a die is thrown, there are two possible outcomes - an odd number or an even number. Therefore, the probability of getting an odd number is 1/2

Consider the numbers 1,2,3,4,5,6,7,8,9,10. If 1 is added to each number, the variance of the numbers so obtained is

An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on two faces is noted. If the result is a tail, a card from a well-shuffled pack of 11 cards numbered 2, 3, 4, ..., 12 is picked and the number on the card is noted. What is the probability that the noted number is either 7 or 8?

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (See figure), and these are equally likely outcomes. What is the probability that it will point at 8? (ii) an odd number? (iii) a number less than 9? (iv) a number greater than 2?

Two different numbers are taken from the set {0,1,2,3,4,5,6,7,8,9,10}dot The probability that their sum and positive difference are both multiple of 4 is x//55 , then x equals ____.

State whether each of the following statement is true or false. Justify your answer. { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.

Mr. A lives at origin on the Cartesian plane and has his office at (4,5) His friend lives at (2,3) on the same plane. Mrs. A can go to his office travelling one block at a time either in the +y or +x direction. If all possible paths are equally likely then the probability that Mr. A passed his friends house is (shortest path for any event must be considere (a) 1/2 (b) 10/21 (c) 1/4 (d) 11/21

State whether each of the following statement is true or false. Justify your answer. { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. Two persons A and B agree to meet at a place between 5 and 6 pm. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independant and at random, then the probability that A and B meet is

Let A={1,2,3,4}, B={1,5,9,11,15,16} and f={(1,5),(2,9),(3,1),(4,5),(2,11)} Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.