Probability — Class 11 solved problems

8 problems from this chapter, each solved step by step.

1. Let X be a discrete random variable, then the variance of X is:

   The variance of a discrete random variable X is given by the formula Var(X) = E[X²] - (E[X])².

2. A coin is tossed three times, consider the following events. A: 'No head appears', B: 'Exactly one head appears' and C: 'Atleast two heads appear'. Do they form

   Yes, the events A, B, and C form a set of mutually exclusive and exhaustive events.

3. If A, B, C are three events associated with a random experiment, prove that P(A B C) & =P(A)+P(B)+P(C)-P(A B)-P(A C) & -P(B C)+P(A B C)

   P(A B C) = P(A)+P(B)+P(C)-P(A B)-P(A C)-P(B C)+P(A B C)

4. Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examina

   (a) The probability that both Anil and Ashima will not qualify the examination is 0.87. (b) The probability that at least one of them will not qualify the exami

5. If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and P(A B) = 0.5, where B denotes the complement of B, then P(B (A B)) is equal to:

   (0.2)/(0.8) = 0.25

6. In a relay race there are five teams A, B, C, D and E. (a) What is the probability that A, B and C finish first, second and third, respectively. (b) What is the

   (a) The probability that A, B and C finish first, second and third, respectively is (1)/(60). (b) The probability that A, B and C are first three to finish (in

7. A committee of two persons is selected from two men and two women. What is the probability that the committee will have (a) no man? (b) one man? (c) two men?

   (a) The probability that the committee will have no man is (1)/(6). (b) The probability that the committee will have one man is (2)/(3). (c) The probability tha

8. Let a sample space be S= _1, _2,, _6. Which of the following assignments of probabilities to each outcome are valid? ccccccc Outcomes & _1 & _2 & _3 & _4 & _5 &

   Assignments (a) and (b) are valid.

More Class 11 chapters

• Sets19 solved
• Relations and Functions26 solved
• Trigonometric Functions33 solved
• Complex Numbers and Quadratic Equations53 solved
• Linear Inequalities9 solved
• Permutations and Combinations49 solved
• Binomial Theorem17 solved
• Sequences and Series34 solved
• Straight Lines19 solved
• Conic Sections68 solved
• Introduction to Three Dimensional Geometry6 solved
• Limits and Derivatives32 solved
• Statistics15 solved

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