Question

A husband and wife both have brown eyes but carry genes that make it possible for their children to
have brown eyes (probability 0.75), blue eyes (0.125), or green eyes (0.125).
a. What is the probability the first blue-eyed child they have is their third child? Assume that the eye
colors of the children are independent of each other.
b. On average, how many children would such a pair of parents have before having a blue-eyed
child? What is the standard deviation of the number of children they would expect to have until the
first blue-eyed child?

Answer 1

Answer:

it's bialogy no maths.

so the offspring have 99.3 % chance to have brown eyes

Answer 2

The probability of having first blue-eyed child as their third child is 0.096

Such pair of parents will have 8 children before having blue-eyed child and

the Standard deviation is 7.48

Step-by-step explanation:

Given :

Probability of having children with brown eyes is 0.75

Probability of having children with blue eyes is 0.125

Probability of having children with green eyes is 0.125

To Find:

a. The probability of having first blue-eyed child as their third child:

Consider X be the number of children until the first blue-eyed child.

Then X can take values 1,2,3,........

P(X = 1) = 0.125

P(X = 2 ) = (1-0.125) x 0.125

P(X = 3) = (1 - 0.125)² x (0.125)

             = (0.875)² x 0.125

              = .765 x .125

              = 0.0957 = 0.096 (As first blue eyed child is the 3 child)

Thus the probability is 0.096

b. Number of children such a pair of parents have before having a blue-eyed  child :

P (X) = 0.125

μ = $\frac{1}{\text{P}(\text{X})}$

  = $\frac{1}{0.125} = 8$

The standard deviation of the number of children they would expect to have until the  first blue-eyed child :

Standard Deviation = $\sqrt{\frac{(1 - \text{P}(\text{X})}{[\text{P}(\text{X})]^2} }$

                                 =$\sqrt{\frac{1-0.125}{(0.125)^2} }$

                               = $\sqrt{\frac{0.875}{0.0156} }$

                                 = $\sqrt{56.089}$

                                 = 7.48

To Learn More...

1. If the varience if a data is 6.25 find its standard deviation​

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2. If the standard deviation of a data is 4.5 and if each value of the data is decreased by 5 then find the new standard deviation​

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