A teacher gave a 3-question multiple choice quiz. Each question had 4 choices to select from. If the a student completely guessed on every p

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A teacher gave a 3-question multiple choice quiz. Each question had 4 choices to select from. If the a student completely guessed on every problem, what is the probability that they will have 2 or less correct answers?

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Thiên Ân 3 years 2021-08-21T18:46:27+00:00 1 Answers 11 views 0

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  1. yenoanh
    0
    2021-08-21T18:47:58+00:00
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    Answer:

    0.9844

    Step-by-step explanation:

    This is a binomial probability problem.

    Probability of getting a correct answer: p = 1/4

    Probability of getting an incorrect answer: q = 3/4

    Number of questions; n = 3

    Thus;

    probability of 2 or less correct answers is; P(x ≤ 2) = P(X = 2) + P(X = 1) + P(X = 0)

    From binomial probability the formula is;

    P(X = x) = C(n, x) × p^(x) × q^(n – x)

    P(X = 2) = C(3, 2) × (¼)² × (¾)¹

    P(X = 2) = 3 × 0.0625 × 0.75

    P(X = 2) = 0.1406

    P(X = 1) = C(3, 1) × (¼)¹ × (¾)²

    P(X = 1) = 3 × 0.25 × 0.5625

    P(X = 1) = 0.4219

    P(X = 0) = C(3, 0) × (¼)^(0) × (¾)³

    P(X = 0) = 0.4219

    P(x ≤ 2) = 0.1406 + 0.4219 + 0.4219

    P(x ≤ 2) = 0.9844

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