Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. find the probability of exactly nine boys in ten births.

0.009765625

Step-by-step explanation:

Binomial probability formula :-

, here P(x) is the probability of getting succeed in x trial, n is the total number of trials and p is the probability of success in each trial.

We assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children.

The probability of of getting a boy = The probability of getting a girl = 0.5

Now, the probability of exactly nine boys in ten births will be :-

Hence, the probability of exactly nine boys in ten births = 0.009765625

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).