Answer the following questions in short: What is the expectation of the number of failures preceding the first success in an infinite series of independent trials with constant probability p of success in each trial?

Answer the following questions in short: Two boys A and B toss a fair coin 4 times each: Find the probability of getting same number of heads.

The probability of success in a single trial of a random experiment is constant and the trial is repeated inependently seven timed, if the probability of 4 successes is equal to 3 successes, find the probability of 3 successes in 5 independent trials of the experiment.

For each natural number k, let C_k denotes the circle with radius k units and centre at the origin. On the circle C_k , a particle moves k units in the counter clockwise direction. After completing its motion on C_k , the particles moves to C_(k + l) , in some well defined manner, where l gt 0 . The motion of the particle continues in this manner. Answer the following question based on above passage : Let l= 1, the particles starts at (1, 0), if the particles crossing the positive direction of the x-axis for the first time on the circle C_n then n is equal to

Find out the correct answer out of the options given against each questions : The variance of 'number of success in a set of 20 Beronullian trials cannot exceed

In which of the following situations, does the list of numbers involved is in the form of a GP? (i) Salary of Sharmila, when her salary is 5,00,000 for the first year and expected to receive yearly increase of 10%. ii) Number of bricks needed to make each step, if the stair case has total 30 steps, provided that bottom step needs 100 bricks and each successive step needs 2 brick less than the previous step. iii) Perimeter of the each triangle, when the mid points of sides of an equilateral triangle whose side is 24 cm are joined to form another triangle, whose mid points in turn are joined to form still another triangle and the process continues indefinitely.

Haemophilia is a sex linked recessive disorder of humans. The pedigree chart given below shows the inheritance of Haemophilia in one family. Study the pattern of inheritance and answer the questions given. (a) Give all the possible genotypes of the members 4, 5 and 6 in the pedigree chart. (b) A blood test shows that the individual 14 is a carrier of haemophilia. The member numbered 15 has recently married the member numbered 14. What is the probability that their first child will be a haemophilic male ? Show with the help of Punnett square.

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