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CBSE Class 12 (Commerce) Probability — practice questions — page 2

Explore 80 free Probability questions in CBSE Class 12 (Commerce) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Probability questions and exercises with answers

Showing questions 31–60 of 80.

Spot the odd one outRead the answer and worked solution →Assertion and reason: the multiplication ruleRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Sort each statement by which idea it describesRead the answer and worked solution →For events E and F with P(F) > 0, P(E|F) is which ratio?Read the answer and worked solution →Three fair coins are tossed. Given the first shows tail, find P(at least two heads).Read the answer and worked solution →If P(B) = 9/13 and P(A ∩ B) = 4/13, what is P(A|B)?Read the answer and worked solution →For an event F with P(F) > 0 in sample space S, P(S|F) equals what?Read the answer and worked solution →If P(E|F) = 0.35, what is P(E'|F)?Read the answer and worked solution →If P(F) = 0.4 and P(E|F) = 0.5, find P(E ∩ F).Read the answer and worked solution →Two cards are drawn one after the other without replacement. P(both aces)?Read the answer and worked solution →A box has 5 red and 3 blue balls. Two are drawn without replacement. P(both red)?Read the answer and worked solution →Events E and F, both with nonzero probability, are independent ifRead the answer and worked solution →E and F are independent, P(E) = 0.3 and P(F) = 0.5. Find P(E ∩ F).Read the answer and worked solution →A card is drawn from 52. Given it is a spade, P(it is an ace)?Read the answer and worked solution →A partition of a sample space must have events that areRead the answer and worked solution →For a nonempty event E, which pair always forms a partition of S?Read the answer and worked solution →How many partitions can a given sample space have?Read the answer and worked solution →E1, E2 partition S: P(E1)=0.6, P(A|E1)=0.2, P(E2)=0.4, P(A|E2)=0.5. Find P(A).Read the answer and worked solution →Bag I: 3 red, 4 black; Bag II: 5 red, 6 black. Pick a bag at random; P(red)?Read the answer and worked solution →When Bayes' theorem is applied, the events E1, ..., En are calledRead the answer and worked solution →In Bayes' theorem, P(Ei) before observing A is called theRead the answer and worked solution →Bayes' theorem is also called the formula for the probability of what?Read the answer and worked solution →What problem did John Bayes solve using conditional probability?Read the answer and worked solution →In which year was Bayes' theorem published posthumously?Read the answer and worked solution →Whose 1654 correspondence laid the first foundation of probability science?Read the answer and worked solution →Three dice are thrown. Which total is more likely, 9 or 10?Read the answer and worked solution →Who discovered the binomial distribution?Read the answer and worked solution →Which Dutch scientist wrote the first book on probability after Pascal and Fermat?Read the answer and worked solution →Which Russian mathematician formulated the axiomatic approach to probability?Read the answer and worked solution →

Worked practice questions

Spot the odd one out

Read exercise and reference answers
Questions
  1. Items
    1. P(E)P(F|E)
    2. P(E) + P(F)
    3. P(F)P(E|F)
    Odd item
    P(E) + P(F)
  2. Items
    1. Prior
    2. Cofactor
    3. Posterior
    4. Partition
    Odd item
    Cofactor
  3. Items
    1. Pairwise disjoint
    2. Union equals S
    3. All equally likely
    4. Nonzero probability
    Odd item
    All equally likely
Each group is one bullet of the summary. Source: syllabus Maths Part II, Ch 13 Probability.

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Assertion and reason: the multiplication rule

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Questions
  1. Reason
    You may condition on either event, provided its probability is nonzero.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    P(E ∩ F) can be written two different ways.
  2. Reason
    Independence makes P(F|E) equal to P(F).
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    For independent events the multiplication rule simplifies.
  3. Reason
    Bayes' theorem has a sum in its denominator.
    Verdict
    Both are true; the reason does not explain the assertion.
    Assertion
    Conditional probability lies between 0 and 1.
Both halves true does not mean one explains the other. Source: syllabus Maths Part II, Ch 13 Probability.

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True or false: the Historical Note

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Questions
  1. Statement is true
    Yes
    Statement
    Pascal and Fermat corresponded about a gambler's problem.
  2. Statement is true
    Yes
    Statement
    Huygens published an early book on probability.
  3. Statement is true
    Yes
    Statement
    Kolmogorov gave probability its axiomatic foundation.
  4. Statement is true
    No
    Statement
    Galileo showed a sum of 9 is likelier than 10 with three dice.
  5. Statement is true
    Yes
    Statement
    Ars Conjectandi was published posthumously.
Straight from the closing note. Source: syllabus Maths Part II, Ch 13 Probability.

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