In a national basketball​ association, the top​ free-throw shooters usually have probability of about 0.90 of making any given free throw. Complete parts​ (a) through​ (c).Find the probability that the player made all 11 free throws and the probability that he made 10 free throws.I set this up like this: 11/11x(.90)to the 11th power, x(1-.90)to the 0 power, is that correct?

In this question you are asking to find the probability of 11 free throws and in the next part you are asking the probability of 10 freed throws,

so first you need to indentify whatprobability  distribution it is so this is the question of binomial distribution. 

Let ud understand how to identify it is the question of binomial distribution

1) Each trial has two outcomes, now in this case when the player throws the ball so it will either be free throw or not free throw that means two possible outcomes.

2) The second thing in binomial is that the number of trials are decided in advance and always given in question,

now in this question they made total 11 throws which is given in question, so number of trials are fixed and given in advance

3)The third feature or property of binomail distribuion is that each trial is indepdent 

now in this question you made eleven throws that means you had total 11 trial, now the outcome of first trial nowhere affects the outcome of second trial. same way the outcome of second trial nowhere affects the third  trial and so on. so all the outcomes are independent which we can also say that all the trials are independent.

4) The probabaility of success on each outcome is same that means in this question the probability of free throw is 0.9 and this probability is same for each trial. if you throw firt ball then also you have 0.9 chances of free throw, if you make second throw then also you have 0.9 probability of free throw and so on.

so these are the four properties which lead us to belive that it is the binomial distribution.

so when we have identified that it is binomial distribution so we can use the formula of binomial distribution to find the probability.

Formula of binomial distribution is as follows.

Let us see the components of formula

first is n , it means number of trials which is given to be 11 in question

next is p, it stands for probability of success it is given in question to be 0.9

q stands for probability of failure 

q = 1 - p

if p = 0.9

q = 1-0.9 = 0.1

x, it stands for requrired probability in question

in the part where they asked probability of all 11 throws to be free throws so x will be 11

in the next part where they asked probability of 10 free throws so x will be 10

so now we will solve both the parts one by one

Probability of making 11 free throws