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Rajasthan Board Class 12 (RBSE) Probability & Statistics — practice questions

Explore 60 free Probability & Statistics questions in Rajasthan Board Class 12 (RBSE) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Probability & Statistics questions and exercises with answers

Showing questions 1–30 of 60.

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 →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead 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 →Assertion and reasonRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →Complete the rule about restricting a domainRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Principal values worked in the chapterRead the answer and worked solution →Order the steps for finding a principal valueRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →Match each identity to the condition it needsRead 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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