# 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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### Learn more about this topic:

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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