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CBSE Class 12 (Commerce) Probability — practice questions

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 1–30 of 80.

A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?Read the answer and worked solution →If P(A) = 0.5, P(B) = 0.6, and P(A ∩ B) = 0.2, then P(A ∪ B) is:Read the answer and worked solution →Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Read the answer and worked solution →Bayes' theorem is essentially used to:Read the answer and worked solution →For a discrete random variable X with values 0, 1, 2 and probabilities 0.3, 0.5, 0.2 respectively, the mean E(X) is:Read the answer and worked solution →In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:Read the answer and worked solution →For a binomial distribution B(n, p), the MEAN and VARIANCE are:Read the answer and worked solution →The number of ways to choose 3 books out of 5 (order does NOT matter) is:Read the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Order the reasoning: from a partition to a posteriorRead the answer and worked solution →Tap every quantity that is a probabilityRead the answer and worked solution →

Worked practice questions

A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?

  1. $1/52$
  2. $2/52$
  3. $1/13$
  4. $1/26$
Show answer and solution

Correct answer: C. $1/13$

P(king | red) = P(red king) / P(red) = (2/52) / (26/52) = 2/26 = 1/13. Conditional probability reduces the sample space.

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If P(A) = 0.5, P(B) = 0.6, and P(A ∩ B) = 0.2, then P(A ∪ B) is:

  1. $0.9$
  2. $1.1$
  3. $1.0$
  4. $0.3$
Show answer and solution

Correct answer: A. $0.9$

We have P(A ∪ B) = P(A) + P(B) − P(A ∩ B). That is P(A ∪ B) = 0.5 + 0.6 − 0.2. So P(A ∪ B) = 0.9.

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Two dice are rolled. The probability of getting AT LEAST ONE SIX is:

  1. One over six i.e. 1/6 exactly
  2. One over three i.e. 1/3 exactly
  3. One over two i.e. 1/2 exactly
  4. Eleven over thirty six (11/36)
Show answer and solution

Correct answer: D. Eleven over thirty six (11/36)

P(at least one 6) = 1 − P(no 6) = 1 − (5/6)² = 1 − 25/36 = 11/36. Complement makes the calculation efficient.

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