Answered

Mr. and Mrs. Doran have a genetic history such that the probability that a child being
born to them with a certain trait is 0.61. If they have four children, what is the
probability that at most two of their four children will have that trait? Round your
answer to the nearest thousandth.

Answer :

Using the binomial distribution, it is found that there is a 0.011 = 1.1% probability that exactly one of their four children will have that trait.

For each children, there are only two possible outcomes, either they have the trait, or they do not. The probability of a children having the trait is independent of any other children, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X=x)=C_{n,x.}p^x.(1-p)^{n-x}[/tex]

[tex]C_{n,x}=\frac{n!}{x!(n-x)!}[/tex]

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • 85% probability of a children having the trait, hence [tex]p=0.85[/tex].
  • They have four children, hence [tex]n=4[/tex]

The probability is P(X = 1), hence:

[tex]P(X=x)=C_{n,x.}p^x.(1-p)^{n-x}[/tex]

[tex]P(X=1)=C_{4,1*}(0.85)^1.(0.15)^3=0.011[/tex]

0.011 = 1.1% probability that exactly one of their four children will have that trait.

A similar problem is given at https://brainly.com/question/24863377

Other Questions