Linear Programming and Probability Quiz

The maximum value of (x + 2y) under the constraints 2x+3y≤6, x + 4y ≤ 4, x, y ≥0 is

The incidence of occupational disease in an industry is such that the workmen have a 10% chance of suffering from it. The probability that out of 5 workmen, 3 or more will contract the disease is

In binomial distribution if n = 25 E (X) = 10, then var (X) =

If a fair coin is tossed 8 times, then the probability that it shows heads at least once is

The probability that a person who undergoes a kidney operation will recover is 0.7. If the six patients who undergoes similar operations, then the probability that half of them will recover is

In a test of Mathematics, there are two types of questions to be answered-short answered and long answered. The relevant data is given below. Time taken to solve: Short answered questions 5 minute; Long answered questions 10 minute. Marks: Short answered questions 3; Long answered questions 5. Number of questions: Short answered questions 10; Long answered questions 14. The total marks is 100. Students can solve all the questions. To secure maximum marks, a student solves x short answered and y long answered questions in three hours, the linear constraints are x≥ 0, y ≥ 0, x ≤10 , y ≤14 and 5x+10y≤180. Then the vertices of a feasible region are

The position of points O (0, 0) and P (2, - 2) in the region of graph of inequation 2x – 3y <5, will be

Find out maximum value of z=5x+7y subject to x + y ≤ 4, 3x + 8y ≤ 24, 10x + 7y ≤ 35, x, y ≥ 0.

A vertex of the linear inequalities 2x+3y≤6, x+4y≤4 and x, y ≥ 0, is

In a box containing 100 eggs, 10 eggs are rotten. The probability that out of a sample of 5 eggs none are rotten, if the sampling is with replacement, is

In binomial probability distribution, mean is 3 and standard deviation is 3/2. Then the probability distribution is

The corner points of the feasible region determined by the system of linear constraints are (0,10), (5,5) (15,15), (0,20). Let z = px + qy, where p, q > 0. Condition on p and q so that the maximum of z occurs at both the points (15, 15) and (0, 20) is

If a fair coin is tossed 8 times, then the probability that it shows heads exactly 5 times is

If for a binomial distribution X~B (7, p) P (X = 1) = P ( X = 2), then p is

An urn contains 4 white and 3 red balls. If 3 balls ar are drawn one by one with replacement and probability of getting exactly two red ball is a(3/b)³, then a+b is

The points which provides the solution to the linear programming problem: Max P = 2x + 3y subject to constraints: x≥ 0, y ≥ 0, 2x + 2y ≤ 9, 2x+y≤7,x+2y≤8 is

Two different kinds of food A and B are being considered to form a weekly diet. The minimum weekly requirement for fats, carbohydrates and proteins are 18, 24 and 16 units respectively. One kg of food A has 4, 16 and 8 units respectively of these ingredients and one kg of food B has 12, 4 and 6 units respectively. The price of food A is Rs.4 per kg and that of food B is Rs.3 per kg. Find out minimum cost.

If p.m.f. of r.v. X is P(X)=4(4-x)/10 , x = 0,1,2,3,4, then Var(X)=

Inequations 3x-y≥3 and 4x-y> 4

The values of x and y for which the objection function z = 3x + 4y under the constraints y ≤x+2,4x ≤ x + 2, 4x +3 + 3y ≤ 12, x > 0 , y ≥ 0 is maximum are

Shaded region is represented by

An insurance agent insures lives of 5 men, all having same age and good health. The probability that a man of this age will survive the next 30 years is known to be 2/3. What is the probability that in the next 30 years almost 3 men will survive?

One coin is thrown 100 times, then the probability of getting head in odd number is

An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success.

For an L.P.P. the feasible region is shown shaded in the figure. Find the maximum value of the objective function z = 5x +7y

The point at which, the maximum value of (3x + 2y) subject to the constraints x+y≤2, x≥0, y ≥0 obtained, is

For a bionomial distribution X~B (n, p) if n=5 and P(X = 1) = 8P (X = 3), then mean of the distribution is

The minimum value of objective function c = 2x + 2y in the given feasible region, is

A die is thrown 6 times. If "getting an odd number" is a success, then the probability of getting 5 successes is....