I am not sure how to do this, just guesssing.

A couple has a 2/3 probability of passing on brown eyes to their children. If they have four children,
what is the probability that none of the children will have brown eyes?

A) 8/27 B) 1/27 C) 1/81 D) 16/81

Would I multiply 2/3^4 thus my answer is D) 16/81

it is a

why do you only multiply to the third power?

Yes, you are on the right track! To find the probability that none of the four children will have brown eyes, you need to multiply the probabilities of each child not receiving the brown eye trait.

Since each child has a 2/3 probability of not inheriting brown eyes, you can calculate the probability of none of them having brown eyes by multiplying (2/3) for each child, four times in a row.

Therefore, the probability can be calculated as (2/3) * (2/3) * (2/3) * (2/3) which is equal to (2/3)^4. Evaluating this expression, you get 16/81.

So, your answer D) 16/81 is correct!