Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads? P (k successes) = Subscript n Baseline C

Question

Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads? P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 6 Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 9 Subscript 9 Baseline C Subscript 6 Baseline (0.5) Superscript 6

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Nho 3 years 2021-07-23T19:08:00+00:00 1 Answers 56 views 0

Answers ( )

  1. minhkhang
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    2021-07-23T19:09:56+00:00
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    Answer:

    P(3) = ^9C_3 * 0.5^3 *0.5^6

    Step-by-step explanation:

    Given

    n = 9 — number of flips

    Required

    P(x = 3)

    The probability of getting a head is:

    p = \frac{1}{2}

    p = 0.5

    The distribution follows binomial probability, and it is calculated using:

    P(x) = ^nC_x * p^x * (1 - p)^{n-x}

    So, we have:

    P(3) = ^9C_3 * 0.5^3 * (1 - 0.5)^{9-3}

    P(3) = ^9C_3 * 0.5^3 *0.5^6

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