Stephen curry plays for the golden state warriors an touts a 90% free throw shooting record. if he shot 12 free throws in a game appromely how many did he miss.

a) Joint ptobability distribution

b) P(X<= 1 and Y <= 1) = P(X<= 1) * P(Y<=1) = 0.56

c) P(X + Y = 0)=0.3

d) P(X + Y <= 1)=0.53

Step-by-step explanation:

We have to construct the joint probability table with the marginal probabilities of X and Y.

X can take values from 0 to 2, and Y can take values from 0 to 4.

We can calculate each point of the joint probability as:

Then, the joint probabilities are:

X=0Y=0Px=0.5Px=0.6P(0,0)=0.3

X=0Y=1Px=0.5Px=0.1P(0,1)=0.05

X=0Y=2Px=0.5Px=0.05P(0,2)=0.025

X=0Y=3Px=0.5Px=0.05P(0,3)=0.025

X=0Y=4Px=0.5Px=0.2P(0,4)=0.1

X=1Y=0Px=0.3Px=0.6P(1,0)=0.18

X=1Y=1Px=0.3Px=0.1P(1,1)=0.03

X=1Y=2Px=0.3Px=0.05P(1,2)=0.015

X=1Y=3Px=0.3Px=0.05P(1,3)=0.015

X=1Y=4Px=0.3Px=0.2P(1,4)=0.06

X=2Y=0Px=0.2Px=0.6P(2,0)=0.12

X=2Y=1Px=0.2Px=0.1P(2,1)=0.02

X=2Y=2Px=0.2Px=0.05P(2,2)=0.01

X=2Y=3Px=0.2Px=0.05P(2,3)=0.01

X=2Y=4Px=0.2Px=0.2P(2,4)=0.04

We can write it in the form of a matrix:

b) From the joint probability P(X<= 1 and Y <= 1) is equal to

We can calculate P(X<= 1) * P(Y<=1)

Both calculations give the same result.

c) Probability of no violations

d) P(X + Y <= 1)