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 ?

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?

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

Consider a game played by 10 prople in which each flips a fair coin at the same time. If all but one of the coins comes up the same, then the add persons wing (e.g., if there are nine tails and one head then person having lead wins.) If such a situation does not occur, the players flips again. Find the probability that game is settled on or after nth toss.

Two persons A and B get together once a weak to play a game. They always play 4 games . From past experience Mr. A wins 2 of the 4 games just as often as he wins 3 of the 4 games. If Mr. A does not always wins or always loose, then the probability that Mr. A wins any one game is (Given the probability of A's wining a game is a non-zero constant less than one).

Suppose the probability for A to win a game against B is 0.4. If A has an option of playing either a “best of 3 games'' or a “best of 5 games match against B, which option should be chosen so that the probability of his winning the match is higher? (No game ends in a draw.)

Two players P_1 , and P_2 , are playing the final of a chase championship, which consists of a series of match Probability of P_1 , winning a match is 2/3 and that of P_2 is 1/3. The winner will be the one who is ahead by 2 games as compared to the other player and wins at least 6 games. Now, if the player P_2 , wins the first four matches find the probability of P_1 , wining the championship.

In a game of chance a player throws a pair of dice and scores points equal to the difference between the numbers on the two dice. Winner is the person who scores exactly 5 points more than his opponent. If two players are playing this game only one time, then the probability that neither of them wins to

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?

Aa n dB play a series of games which cannot be drawn and p , q are their respective chance of winning a single game. What is the chance that A wins m games before B wins n games?

Aa n dB play a game of tennis. The situation of the game is as follows: if one scores two consecutive points after a deuce, he wins; if loss of a point is followed by win of a point, it is deuce. The chance of a server to win a point is 2/3. The game is a deuce and A is serving. Probability that A will win the match is (serves are change after each game) a. 3//5 b. 2//5 c. 1//2 d. 4//5