StudyRaah StudyRaah XI-XIIOpen StudyRaah

Maharashtra State Board · HSC Commerce · Class 11 (Std XI)

Class 11 Maths and Statistics Part 2 Chapter 7: Probability

Short notes, key concepts, quick revision and practice MCQs with answers

Probability measures the chance of an event on a scale from 0 to 1. The chapter defines random experiments, sample spaces and types of events, the algebra of events, the classical definition of probability, the addition theorem, conditional probability, the multiplication theorem, independent events and odds.

Key concepts: Probability

Random experiment and sample space
An action whose possible results are known in advance but the actual result cannot be predicted. The set of all outcomes is the sample space S; each element is a sample point.
Events
An event is a subset of S. Elementary (single outcome), sure event (S itself), impossible event (∅) and the complementary event A′ (outcomes not in A).
Algebra of events
A ∪ B: at least one of A, B occurs. A ∩ B: both occur. Mutually exclusive: A ∩ B = ∅. Exhaustive: A ∪ B = S.
Classical probability
For equally likely outcomes, P(A) = n(A)/n(S). 0 ≤ P(A) ≤ 1, P(S) = 1, P(∅) = 0 and P(A′) = 1 − P(A).
Addition theorem
P(A ∪ B) = P(A) + P(B) − P(A ∩ B). For mutually exclusive events, P(A ∪ B) = P(A) + P(B).
Conditional probability
P(A/B) = P(A ∩ B)/P(B), P(B) ≠ 0: the probability of A given that B has occurred.
Multiplication theorem and independence
P(A ∩ B) = P(A) P(B/A) = P(B) P(A/B). A and B are independent if P(A ∩ B) = P(A) P(B).
Odds
Odds in favour of A = n(A) : n(A′). If odds in favour are a : b, then P(A) = a/(a + b).

Quick revision: important points

Practice MCQs with answers

  1. The probability of getting a head when a fair coin is tossed is:

    1. 0
    2. 1/4
    3. 1/2
    4. 1
    Show answer

    Answer: C. 1/2
    One favourable outcome out of two.

  2. The probability of getting a number greater than 4 on a die is:

    1. 1/6
    2. 1/3
    3. 1/2
    4. 2/3
    Show answer

    Answer: B. 1/3
    5 and 6: 2/6 = 1/3.

  3. When two coins are tossed, the number of sample points is:

    1. 2
    2. 3
    3. 4
    4. 8
    Show answer

    Answer: C. 4
    HH, HT, TH, TT.

  4. The probability of an impossible event is:

    1. 0
    2. 1
    3. 1/2
    4. −1
    Show answer

    Answer: A. 0
    It contains no sample point.

  5. If P(A) = 0.3, then P(A′) is:

    1. 0.3
    2. 0.7
    3. 1.3
    4. 0.09
    Show answer

    Answer: B. 0.7
    1 − 0.3 = 0.7.

All Class 11 Maths and Statistics chapters

Class 11 Maths and Statistics notes: all chapters