Suppose you drop a die at random on the rectangular region shown in figure. What is the probability that it will land inside the circle with diameter 1m?

In a bolt factory, machines M_(1), M_(2), M_(3) manufacture respectively 25, 35 and 40 percent of the total product. Of their output 5, 4 and 2 percent respectively are defective bolts. One bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine M_(3) ?

From the employees of a company, 5 person are selected to repreent them in the managing committee of the company. Particular of five persons are as follows: {:("S.No.","Name ","sex","age in years"),(1.,"harish ",M,30),(2. , "Rohon",M,33),(3.,"sheetal",F,46),(4.,"Alis",F,28),(5. ,"Salim",M,41):} A person is selected at random from this group to act as a spokespersons. What is the probability that the spokespersons will be either male or over 35 years?

Suppose we throw a die once. (1) What is the probability of getting a number greater than 4? (in) What is the probability of getting a number less than or equal to 4?

A box contains N coins, m of wiich are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is 1/2, while it is 2/3 when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. What is the probability that the coin drawn is fair ?

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

Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?