Question

Assuming that Caleb makes 70% of his free throws and shoots 10 free throws in a game, what is the probability that he will make?

a) All 10 of his free throws in a game?
b) Make seven or more of his free throws in a game?
c) Find the mean number of free throws Caleb would make in the game.

Answer 1

You can solve this using a binomial distribution

Answer 2

how do i do that

Answer 3

we know the probability of making any given free throw is .70

Answer 4

yes

Answer 5

lets define
S = makes a free throw. F = fails to make a free throw

Answer 6

S is short for success, F for fail

Answer 7

okay

Answer 8

a) we want the probability
SSS SSS SSS SS , ten S's in a row
each S has probability of 0.7
so you get
0.7 * 0.7 * 0.7 * ... *0.7 = 0.7^10

Answer 9

so the answer to a is 0.0282475249

Answer 10

correct

Answer 11

okay so b?

Answer 12

b) is a bit more tricky
you want seven successful free throws

for example:

SSSSSSSFFFF

Answer 13

seven or more

Answer 14

right, so we also need eight S's, nine S's , and ten S's

Answer 15

okay so we do .7^7 and .7^8 and .7^9 and .7^10?

Answer 16

we also need probability of failures too

Answer 17

for the case of exactly seven free throws
SSS SSS S FFF
.7^7 * .3^3
and you're not done, there are also more cases

the order counts, you can have
FFF SSS F SSSS

Answer 18

0.0022235661

Answer 19

so its pretty hard to do this by writing out all the possibilities.
instead we use a formula, binomial formula

Answer 20

Let's define a variable X = number of successful free throws (out of ten free throws)

Answer 21

okay

Answer 22

b) is asking P( X >= 7 ) = P( X = 7 ) + P( X= 8) + P( X = 9) + P( X = 10)

Answer 23

okay

Answer 24

So the general formula is
P( X = k) = nCk * p^k * (1-p)^(n-k)

here n = number of trials
p = probability of success

Answer 25

what is C and k?

Answer 26

k is what you want , here k is 7. C stands for choose

Answer 27

for example
P( X = 7) = (10 choose 7) * .7^7 * (.3)^(3)

Answer 28

oh okay

Answer 29

so
P( X >= 7 )
= P( X = 7 ) + P( X= 8) + P( X = 9) + P( X = 10)
= (10 choose 7) * .7^7 * (.3)^(3) + (10 choose 8 ) * .7^8 * (.3)^2 + (10 choose 9) * .7^9 *.3^1 + (10 choose 10)* (.7^10)(.3)^0

Answer 30

here it is easier to read
http://www.wolframalpha.com/input/?i=evaluate+%2810+choose+7%29+*+.7^7+*+%28.3%29^%283%29+%2B+%2810+choose+8+%29+*+.7^8+*+%28.3%29^2+%2B+%2810+choose+9%29+*+.7^9+*.3^1+%2B+%2810+choose+10%29*+%28.7^10%29%28.3%29^0

Answer 31

oh okay i see so the answer to b is 0.6496107184

Answer 32

he left, what the freckle

Answer 33

sometimes they come back, or they have technical issues

Answer 34

I'm back sorry

Answer 35

did that make sense so far?

Answer 36

yes

Answer 37

mine doesn't die

Answer 38

you have to multiply by the binomial coefficient because you have more cases

Answer 39

nin, what browser youre using? im using mozilla

Answer 40

so the answer is not 0.6496107184?

Answer 41

thats correct

Answer 42

what is the binomial coefficient

Answer 43

that tells you how many ways you can rearrange S and F

Answer 44

if you have seven S's and three F's, how many ways you can rearrange them
I can't write them all out , since there are 120 ways , or 10 choose 7 ways

Answer 45

imconfused again

Answer 46

which part is confusing

Answer 47

how to multiply the binomial coeffienct

Answer 48

you have to find the binomial coefficient

Answer 49

or evaluate it, i should say

Answer 50

im m sorry i don't get it

Answer 51

@perl