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Probability

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Conditional probability, multiplication theorem on probability

Subtopic

Conditional probability, multiplication theorem on probability under Probability for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Two dice are thrown. If the sum of the numbers is 7, find the probability that one of the dice shows 3.

    A.

    16\frac{1}{6}

    B.

    13\frac{1}{3}

    C.

    27\frac{2}{7}

    D.

    12\frac{1}{2}

  2. 2.

    Given P(A)=0.6P(A) = 0.6, P(B)=0.2P(B) = 0.2 and P(A∣B)=0.5P(A|B) = 0.5, calculate P(B∣A)P(B|A).

    A.

    13\frac{1}{3}

    B.

    16\frac{1}{6}

    C.

    12\frac{1}{2}

    D.

    14\frac{1}{4}

  3. 3.

    If P(A)=P(B)=xP(A) = P(B) = x and P(A∩B)=x2P(A \cap B) = x^2, then AA and BB are always:

    A.

    Mutually exclusive

    B.

    Dependent

    C.

    Independent

    D.

    Equal

Download the worksheet for Probability - Conditional probability, multiplication theorem on probability to practice offline. It includes additional chapter-level practice questions.

Independent events, total probability, Bayes’ theorem

Subtopic

Independent events, total probability, Bayes’ theorem under Probability for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If AA and BB are independent events such that P(A)=1/2P(A) = 1/2 and P(B)=1/3P(B) = 1/3, then P(A∪B)P(A \cup B) is:

    A.

    2/32/3

    B.

    5/65/6

    C.

    1/61/6

    D.

    1/21/2

  2. 2.

    A card is drawn from a deck of 52. EE: the card is a spade, FF: the card is an ace. Are EE and FF independent events?

    A.

    Yes

    B.

    No

    C.

    Maybe

    D.

    Depends on how they are drawn

  3. 3.

    If P(A)=0.2P(A) = 0.2 and P(B)=0.6P(B) = 0.6, and AA and BB are independent, what is P(A′∩B′)P(A' \cap B')?

    A.

    0.32

    B.

    0.12

    C.

    0.48

    D.

    0.68

Download the worksheet for Probability - Independent events, total probability, Bayes’ theorem to practice offline. It includes additional chapter-level practice questions.

Random variable and its probability distribution

Subtopic

Random variable and its probability distribution under Probability for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The mean of a random variable XX is 10. What is E(2X+5)E(2X + 5)?

    A.

    20

    B.

    25

    C.

    15

    D.

    10

  2. 2.

    If XX represents the outcome of rolling a fair die, then P(X is even)P(X \text{ is even}) is:

    A.

    16\frac{1}{6}

    B.

    13\frac{1}{3}

    C.

    12\frac{1}{2}

    D.

    23\frac{2}{3}

  3. 3.

    A random variable XX has P(X=1)=0.5P(X=1)=0.5 and P(X=2)=0.5P(X=2)=0.5. Find Var(X)Var(X).

    A.

    0.25

    B.

    0.5

    C.

    0.75

    D.

    0

Download the worksheet for Probability - Random variable and its probability distribution to practice offline. It includes additional chapter-level practice questions.

Mean of a random variable

Subtopic

Mean of a random variable under Probability for Grade 12 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    A random variable XX takes the values 1,2,31, 2, 3 with probabilities k,2k,3kk, 2k, 3k. The mean of XX is:

    A.

    2.0

    B.

    7/3

    C.

    2.5

    D.

    1.5

  2. 2.

    A random variable XX has a mean of 5. What is the mean of Y=2X−3Y = 2X - 3?

    A.

    7

    B.

    10

    C.

    13

    D.

    5

  3. 3.

    A random variable XX takes values 1,10,1001, 10, 100 with probabilities 0.7,0.2,0.10.7, 0.2, 0.1 respectively. The mean is:

    A.

    37

    B.

    12.7

    C.

    111/3

    D.

    25.5

Download the worksheet for Probability - Mean of a random variable to practice offline. It includes additional chapter-level practice questions.