The probability that a randomly chosen citizen-entity of Cygnus is of pension age† is approximately 0.7. What is the probability that, in a

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The probability that a randomly chosen citizen-entity of Cygnus is of pension age† is approximately 0.7. What is the probability that, in a randomly selected sample of four citizen-entities, all of them are of pension age?

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Kinsley 2 weeks 2021-09-10T11:06:30+00:00 1 Answer 0

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    2021-09-10T11:07:57+00:00

    Answer: 0.2401

    Step-by-step explanation:

    The binomial distribution formula is given by :-

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

    where P(x) is the probability of x successes out of n trials, p is the probability of success on a particular trial.

    Given : The probability that a randomly chosen citizen-entity of Cygnus is of pension age† is approximately: p =0.7.

    Number of trials  : n= 4

    Now, the required probability will be :

    P(x=4)=^4C_4(0.7)^4(1-0.7)^{4-4}\\\\=(1)(0.7)^4(1)=0.2401

    Thus, the probability that, in a randomly selected sample of four citizen-entities, all of them are of pension age =0.2401

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