Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another. What is the probability that both will visit the shop on the same day?

Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another. What is the probability that both will visit the shop on consecutive days?

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that  (i) the youngest is a girl, (ii) at least one is a girl?

In a hospital, on the same day-5 children were born to different couples. What is the probability of all 5 children being boys?

In a family there are 4 children. Find the probability that (i) all of them will have different birthdays, (ii) two of them will have the same birthday (1 year = 365 days).

Find the probability that the birthday of 7 persons will fall on 7 different days of the week assuming equal probability for each of these days.

In family there are 5 children. Find the probability that (i) all of them will have different birthdays (ii) two of them will have the same birthday and (iii) at least two of them will have the same birthday (1 year = 365 days).

Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any change in speed, as shown in Fig. 5.6. What is (i) the direction of the force on the wall due to each ball? (ii) the ratio of the magnitudes of impulses imparted to the balls by the wall ?

(Manufacturing problem): A manufacturer has three machines. I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for atleast 5 hours a day. She produces only two items M and N each requiring the sue of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machies are given in the follownig table: She makes a profit of Rs. 600 and Rs. 400 on items M and N respectively. How many of each item should be produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum profit?

The planet Mars has two moons, phobos and delmos. (i) phobos has a period 7 hours, 39 minutes and an orbital radius of 9.4 xx 103 km. Calculate the mass of mars. (ii) Assume that earth and mars move in circular orbits around the sun, with the martian orbit being 1.52 times the orbital radius of the earth. What is the length of the martian year in days ?