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Mathematics: Probability and Statistics Flashcards

6 cards from real GAOKAO practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

    Answer: 68%

    The empirical (68-95-99.7) rule states that ~68% of data lies within ±1 standard deviation of the mean.

  2. A box contains 4 white and 6 black marbles. Two marbles are drawn without replacement. What is the probability both are white?

    Answer: 2/15

    P = (4/10) × (3/9) = 12/90 = 2/15.

  3. Which of the following correctly describes the variance of a dataset?

    Answer: The average of squared deviations from the mean

    Variance is defined as the average of the squared deviations of each data point from the mean.

  4. If a random variable X follows a binomial distribution with n = 10 and p = 0.5, what is E(X)?

    Answer: 5

    The expected value of a binomial distribution is E(X) = n × p = 10 × 0.5 = 5.

  5. A frequency table shows scores: 60 (5 students), 70 (8 students), 80 (7 students), 90 (5 students). What is the mode?

    Answer: 70

    The mode is 70 because it appears most frequently (8 students).

  6. Two independent events A and B have P(A) = 0.5 and P(B) = 0.6. What is P(A ∩ B)?

    Answer: 0.30

    For independent events, P(A ∩ B) = P(A) × P(B) = 0.5 × 0.6 = 0.30.