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    in a certain​ country, the true probability of a baby being a is . among the next randomly selected births in the​ country, what is the probability that at least one of them is a ​?

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    Answer in Statistics and Probability for Vladimyr Lubin #143161

    Answer to Question #143161 in Statistics and Probability for Vladimyr Lubin

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    Question #143161

    In a certain​ country, the true probability of a baby being a girl is 0.473. Among the next four randomly selected births in the​ country, what is the probability that at least one of them is a boy​?

    The probability is ?. Round to 3 decimal

    Expert's answer

    Probably that among the next four randomly selected births in the​ country baby being a girl is

    0.473^4=0.050054665441

    0.473 4

    =0.050054665441. In another way will born at least 1 boy, it means among the next four randomly selected births in the​ country probability that at least one of them is a boy equals

    1-0.473^4 = 1-0.050054665441 = 0.949945334559 \approx 0.950

    1−0.473 4

    =1−0.050054665441=0.949945334559≈0.950

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    SOLUTION: In a certain country, the true probability of a baby being a girl is 0.483. Among the next seven randomly selected births in the country, what is the probability that at least one

    Algebra ->  Probability-and-statistics -> SOLUTION: In a certain country, the true probability of a baby being a girl is 0.483. Among the next seven randomly selected births in the country, what is the probability that at least one       Log On

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    In a certain country, the probability of a baby being a boy is 0.533. Among the next eight randomly selected births in the country, what is the probability that at least one of them is a girl?

    Answer to: In a certain country, the probability of a baby being a boy is 0.533. Among the next eight randomly selected births in the country, what...

    Probability distribution

    In a certain country, the probability of a baby being a boy is 0.533. Among the next eight...

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    Question:

    In a certain country, the probability of a baby being a boy is 0.533. Among the next eight randomly selected births in the country, what is the probability that at least one of them is a girl?

    Binomial Distribution:

    Binomial distribution formula for any random variable

    X X is given as: P ( X ) = n C r p r q n − r P(X)=nCrprqn−r , where n n

    is the total number of trials,

    r r

    is the number of specific trials,

    p p

    is the probability of success, and

    q q

    is the probability of failure.

    Answer and Explanation:

    Given:

    The probability of a baby being a boy is

    0.533 0.533 .

    We have to find the probability that at least one of them is a girl among the next eight randomly selected births in the country.

    We have, n = 8 n=8 p ( b o y ) = 0.533 p(boy)=0.533

    We know that sum of probability is$1$. Therefore,

    p ( g i r l ) = 1 − p ( b o y ) = 1 − 0.533 = 0.467

    p(girl)=1−p(boy)=1−0.533=0.467

    The probability that at least one of them is a girl among the eight randomly selected births is given as:

    p ( a t l e a s t o n e g i r l ) = 1 − p ( a l l o f t h e m i s b o y s ) = 1 − 8 C 8 ( 0.533 ) 8 ( 0.467 ) 8 − 8 = 1 − ( 0.533 ) 8 = 0.9934

    p(atleastonegirl)=1−p(allofthemisboys)=1−8C8(0.533)8(0.467)8−8=1−(0.533)8=0.9934

    Hence, the required probability is

    0.9934 0.9934 .

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    Probability Distribution: Definition, Formula & Example

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    Chapter 20 / Lesson 11

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    Explore probability distribution, which shows the likelihood of multiple outcomes. Review definitions and formulas for probability and probability definition, examine non-uniform probability and cumulative distribution, and see examples.

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