An artillery targer may be either at point I with probability `8//9` or at point II with probability `1//9.` Wc have 55 shells, each of which can be fired either rat point I or II. Each shell may hit the target, independent of the other shells, with probability `1//2.` Maximum number of shells must be fired at point I to have maximum probability is

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is i. 9 ii) 12.

Which of the following arguments are correct and which are not correct? Give reasons. i) If two coins are tossed simultaneously there are three possible outcomes - two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3 ii)If a die is thrown, there are two possible outcomes - an odd number or an even number. Therefore, the probability of getting an odd number is 1/2

India play two matches each with West Indies and Australia. In any match the probabilities of India getting 0,1 and 2 points are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is 0. 0875 b. 1//16 c. 0. 1125 d. none of these

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

(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?

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 and these are equally likely outcomes. What is the probability that it will point at 8?

A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The disce are similar in shape and size. A disc is drawn at rendom from the bag. Calculate the probability that it will be (i) red, (ii) yellow, (iii) blue, (iv) not blue, (v) either red or blue.

Three boxes of the same appearance have the following proportions of white and black balls- box I: 1 white and 2 black, box II : 2 white and 1 black, box III : 2 white and 2 black. One of the boxes is selected at random and one ball is drawn randomly from it. It turns out to be white. What is the probability that the third box is chosen ?

Which line is having the greatest inclination with the positive direction of the x-axis? (i) Line joining the points (1, 3) and (4, 7) (ii)Line 3x-4y+3=0