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15 December, 08:02

Suppose 60% of jurors come to a just decision. In a jury of ten people, what is the probability more than half come to a just decision?

A. 0.3669

B. 0.3823

C. 0.6177

D. 0.6331

E. 0.8494

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  1. 15 December, 10:41
    0
    D. 0.6331

    Step-by-step explanation:

    Use binomial probability:

    P = nCr pʳ qⁿ⁻ʳ

    where n is the number of trials,

    r is the number of successes,

    p is the probability of success,

    and q is 1-p, the probability of failure.

    More than half of 10 jurors is 6, 7, 8, 9, and 10. Find the probability of each.

    If r = 6:

    P = ₁₀C₆ (0.6) ⁶ (0.4) ⁴

    P = 0.2508

    If r = 7:

    P = ₁₀C₇ (0.6) ⁷ (0.4) ³

    P = 0.2150

    If r = 8:

    P = ₁₀C₈ (0.6) ⁸ (0.4) ²

    P = 0.1209

    If r = 9:

    P = ₁₀C₉ (0.6) ⁹ (0.4) ¹

    P = 0.0403

    If r = 10:

    P = ₁₀C₁₀ (0.6) ¹⁰ (0.4) ⁰

    P = 0.0060

    Therefore, the total probability is:

    P = 0.2508 + 0.2150 + 0.1209 + 0.0403 + 0.0060

    P = 0.6330
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