Question

Mr. and Mrs. Doran have a genetic history such that the probability that a child being
born to them with a certain trait is 2/5. If they have seven children, what is the
probability that exactly six of their seven children will have that trait? Round your
answer to the nearest thousandth.

Answer 1

Answer: $0.017$

Step-by-step explanation:

Given

the Probability that a child will born with a certain trait is $\frac{2}{5}$

So, the probability that child does not possess that certain trait is $\frac{3}{5}$

The probability that exactly six of their children has that trait is

$\Rightarrow (\dfrac{2}{5})^6\cdot (\dfrac{3}{5})$

For 7 children it is

$\Rightarrow 7\times (\dfrac{2}{5})^6\cdot (\dfrac{3}{5})\\\\\Rightarrow 0.017$