In recent years it was thought that approximately 1 in 110 c

In recent years it was thought that approximately 1 in 110 children exhibited some form of autism. The most recent CDC study concluded that the proportion may be as high as 1 in 88. If indeed these new figures are correct, choose 3 children at random and find these probablities

a. What is the probability that none have autism?

b. what is the probability that at least 1 has autism?

c. choose 10 children at random. What is the probability that at least 1 has autism?

Solution

a. What is the probability that none have autism?

Given X follows Binomial distribution with n=3 and p=1/88=0.0113636

P(X=x)=3Cx*(0.0113636^x)*((1-0.0113636)^(3-x))

So P(X=0) =3C0*(0.0113636^0)*((1-0.0113636)^(3-0)) =0.9662951

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b. what is the probability that at least 1 has autism?

P(X>=1)=1-P(X=0)

=1-0.9662951

=0.0337049

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c. choose 10 children at random. What is the probability that at least 1 has autism?

Given X follows Binomial distribution with n=10 and p=1/88=0.0113636

P(X=x)=10Cx*(0.0113636^x)*((1-0.0113636)^(10-x))

So P(X>=1)=1-P(X=0)

=1-10C0*(0.0113636^0)*((1-0.0113636)^(10-0))

=0.1079977