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COMEDK Probability — practice questions — page 2

Explore 59 free Probability questions in COMEDK 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 31–59 of 59.

Binomial distribution: P(X = k) for n trials, success probability p:Read the answer and worked solution →E(X) and Var(X) for fair coin tossed n times (success = heads, p = 0.5):Read the answer and worked solution →Two cards drawn from a deck (no replacement). P(both kings):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 →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 →

Worked practice questions

Binomial distribution: P(X = k) for n trials, success probability p:

  1. n × p
  2. p^k × (1-p)^(n-k)
  3. C(n,k) × p^k × (1-p)^(n-k)
  4. n^k × p
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Correct answer: C. C(n,k) × p^k × (1-p)^(n-k)

**Binomial:** P(X = k) = C(n, k) × p^k × (1-p)^(n-k). For n coin flips, prob of exactly k heads with p = 0.5 success rate.

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E(X) and Var(X) for fair coin tossed n times (success = heads, p = 0.5):

  1. E = n/2, Var = n/2
  2. E = n/2, Var = n/4
  3. E = n, Var = 1
  4. E = 0.5, Var = 0.25
Show answer and solution

Correct answer: B. E = n/2, Var = n/4

Binomial(n, 0.5): E(X) = np = n/2. Var(X) = np(1-p) = n × 0.5 × 0.5 = n/4.

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Two cards drawn from a deck (no replacement). P(both kings):

  1. 1/13
  2. 16/2652
  3. 1/221
  4. 16/52²
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Correct answer: C. 1/221

P(1st king) = 4/52. P(2nd king | first king) = 3/51. P(both) = (4/52)(3/51) = 12/2652 = 1/221.

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More Mathematics topics

GeometrySequencesProbability & StatisticsBinomial TheoremSequences and SeriesLinear ProgrammingLimits and ContinuityConic Sections