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?

A missing helicopter is reported to have crashed somewhere in the rectangular region as shown in figure. What is the probability that it crashed inside the lake shown in the figure?

A missing helicopter is reported to have crashed somewhere in the rectangular region as shown in the figure. What is the probability that it crashed inside the lake shown in the figure?

Let the matrix M=[{:(x,y),(z,1):}] If x,y and z are chosen at random from the set {1.2.3}, and repetition is allowed (i.e.,x=y=z), what is the probability that the given matrix M is a singular matrix?

Some boys are playing a game, in which the stone thrown by them landing in a circular region (give in the figure ) is considered as win and landing other than the circular region is considered as loss. What is the probability to win the game ?

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?

Suppose that the reliability of a HIV test is specified as follows. Of people having HIV, 90% of the test detect the diséase but 10% go undetected. Of people free of HIV, 99% of the test judged HIV (-ve) but 1% are diagnosed as showing HIV (+ ve). From a large population of which 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist report him/her as HIV (+ve) What is the probability that the person actually has HIV?

A box contains N coins m of which 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. A point is selected at random inside a circle. The probability that the point is closer to the center of the circle than to its circumference is