Question

8. Problem: Michael makes 90% of his free throws in basketball. If he shoots 20 free throws, and if his chance of making each one is independent of the other shots, what is the probability that he makes… (3 pts.)
a. all 20?
b. exactly 18?
c. at least 18?

Answer 1

For each throw, there is a 90% change it will make it.
So for one throw, the probability is 90%.

If he makes 20 throws and there is a 90% chance that each one will go in, what are the chances that they all will go in?

My guess would be 90%. What are your thoughts?

Answer 2

Working with decimals is easier when doing calculations.
So for one shot the probability is 0.9.

Answer 3

If he/she is throwing 20, then the probably that each one will make it is 0.9, not 100%.
So I think x/0.9 = 20/20, x being the probability that this will occur.

Answer 4

I'd get a second opinion though, I'm not sure about this. :D

Answer 5

a. The probability of making all 20 shots is given by
\[P(all\ 20)=0.9^{20}=you\ can\ calculate\]
b. The probability of making exactly 18 shots out of 20 is given by
\[P(18\ out\ of\ 20)=20C18\ \times0.9^{18}\ \times\ 0.1^{2}=\frac{20\times19}{2}\times0.9^{18}\ \times0.1^{2}=you\ can\ calculate\]
c. The probability of making at least 18 shots is found by adding the probabilities of making exactly 18 shots, exactly 19 shots and all 20 shots.

Answer 6

If you want to see a graphical illustration of the concept behind @kropot72's excellent answer, see http://openstudy.com/study#/updates/52e429e6e4b096fa40599c7a