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MelaIvy
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Tyro
Asked: 2021-04-12T05:57:14+00:00 In: ,

Statistics and Probability: Binomial Probability Distribution

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A coin is tossed 4 times. Find the probability that exactly 2 heads will appear.

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2 Answers

  2. acedstud
    This answer was edited.

    Let X be a random variable representing the number of heads that appear in n coin tosses, then the probability of success (p) is \dfrac{1}{2}=0.5.

    The probability that a binomial distributed variable X with the number of tries, n, and the probability of success, p is equal to a value x is given by P(X=x)=^nC_xp^x(1-p)^{n-x}.

    Here, n=4, so the probability that exactly two heads will appear (x=2) is given by P(X=2)=^4C_2(0.5)^2(1-0.5)^{4-2}=6\times0.25(0.5)^2=0.375

    Therefore, the probability that exactly two heads will appear is 0.375.

  4. Sengemegz
    Moderator

    2^{4}=16

    The 4 stands for 4 tosses while the 2 stands for 2 outcomes(H,T)

    Sample space={HHHH, HHHT,HHTH,HHTT,HTHH,HTHT,HTTH,HTTT,THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT}

    Prob.(exactly two heads) = \frac {6}{16}

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