Revision - Linear Programming & Probability

Grade 12 Maths Higher — Revision - Linear Programming & Probability: 25 practice questions with instant scoring and explanations.

1. In a linear programming problem, the objective function is always:
2. The feasible region of a linear programming problem is:
3. If the feasible region is bounded, the objective function attains its optimum at:
4. Maximum of Z = 3x + 4y subject to x + y ≤ 4, x ≥ 0, y ≥ 0 is:
5. The corner points of a feasible region are (0, 0), (5, 0), (3, 4), (0, 5). The maximum of Z = 2x + 5y is:
6. Minimum of Z = 3x + 5y subject to x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0 is:
7. If A and B are independent events with P(A) = 0.3 and P(B) = 0.4, then P(A ∩ B) is:
8. If P(A) = 1/2 and P(B) = 1/3 and A, B are mutually exclusive, then P(A ∪ B) is:
9. If P(A|B) = 0.6 and P(B) = 0.5, then P(A ∩ B) is:
10. Two dice are rolled. The probability that the sum is 7 is:
11. A bag has 5 red and 3 blue balls. Two are drawn without replacement. P(both red) is:
12. A die is rolled. Given that the outcome is odd, the probability it is 3 is:
13. If X is a random variable with E(X) = 5 and Var(X) = 4, then E(X²) is:
14. For a binomial distribution B(n, p), the mean is:
15. For B(10, 0.4), the variance is:
16. If P(A) = 0.4, P(B) = 0.5 and P(A ∩ B) = 0.2, then A and B are:
17. Bayes' theorem gives:
18. A coin is tossed 3 times. P(exactly 2 heads) is:
19. The probability distribution of a binomial variable has Σp(x) equal to:
20. If the feasible region of an LPP is unbounded and Z has a maximum, then maximum must occur at:
21. Maximum of Z = x + 2y subject to 2x + y ≤ 6, x + 2y ≤ 6, x, y ≥ 0 is:
22. A family has 2 children. The probability that both are girls given at least one is a girl is:
23. For B(n, p), if n = 5 and p = 1/2, then P(X = 3) is:
24. If P(E) = 0.05, the odds against E are:
25. The minimum of Z = 4x + 3y subject to 3x + 2y ≥ 160, 5x + 2y ≥ 200, x, y ≥ 0 is: