Basketball Probability

Teams

100

The heat has a 6% chance of winning any game. What is the probability that they will win the next 2 games?

.06 x .06 = .36%

200

The Golden State Warriors collectively have an average of 20% 3 pt. shots made of all 3 pt. shots taken. What is the probability that it will take any given player 4 attempts to make a 3 pt. shot?

geometpdf(.2,4) = 10.24%

300

The University of Kentucky has a 92% chance of winning the National Championship each year. What is the probability that they win exactly 3 of the next 7 years?

(7c3) x .92^3 x .08^4 = .112%

400

The probability of the Milwaukee Bucks winning a game is 30%. The probability of them racing each other with Big Wheels is 80% if they win. The probability of them racing if they lose 99%. What is the probability that the bucks will race in big wheels?

P(win) = .3 P(lose) = .7 P(win/race) = .8 P(lose/race) = .99 P(win/norace) = .2 P(lose/norace) = .01 (.3 x .8) + (.7 + .99) = .933

500

The Celtics want to simulate the odds of any given team member making a free throw for next season. Based on data taken from the current season, the average probability of a Celtics player making a free throw is 60%. What is one correct procedure for designing a simulation to estimate this probability?

Key component: whether a shot is made or not. Assumptions: P(shot made) = .6 P(no shot) = .4 All shots are independent from each other Model: Random # 1-10 1-6 = shot made 7-10 = no shot Trial: Randomly generate # 1-10 5 times T1: 1 6 4 8 6 4 shots made of 5 = 80% T2: 9 10 6 9 2 2 shots made of 5 = 40% T3: 8 3 6 6 8 3 shots made of 5 = 60% Complete 25-30 trials and record results. Find the average of the averages.

Players

100

Dwight Howard has a 40% chance of getting 5 or more fouls in a game. If he receives at least 5 fouls in a game, he has an 80% chance of getting a technical foul. If he gets less than 5 fouls in a game, the probability of him getting a technical foul is 40%. What is the probability of Dwight Howard receiving a technical foul?

P(5+) = .4 P(<5) = .6 P(T&5+) = .32 P(T&<5) = .24 P(NT&5+) = .08 P(NT&<5) = .36 .32+.24 = 56%

200

The Milwaukee Bucks have an 8% chance of getting the first overall lottery pick. What is the probability that 5 teams or more will select a player before the Bucks are able to select?

1 - geometcdf(.08, 4) = 71.64%

300

Every shot that Festus Ezeli takes has 68% chance of going in. What is the probability that Ezeli makes less than 10 shots when he shoots 20 shots?

Binomcdf(20, .68, 9) = .0279 = 2.79%

400

The Oklahoma City Thunder got their name for a reason. Kevin Durant has a 92% chance of making all of his free throws when it is thundering. When it isn't thundering, there is a 65% chance that he makes all of his free throws. There is a 50% chance of thunder during the next game. What is the probability that Kevin Durant doesn't make all of his free throws?

P(T) = .5 P(NT) = .5 P(T&M) = .04 P(NT&M) = .175 P(Miss) = .04 + .175 = .215

500

Kevin Garnett does a pregame ritual 95% of games. When he does it, his team has a 67% of winning. When he doesn't, his team has a 45% chance of winning. What is the probability of his team winning when he doesn't do his pregame ritual?

P(No Ritual)= .05 P(Winning given No Ritual)= .45 (.05)(.45)= .0225 = 2.25%

Shots

100

A 2 pt. shot is accompanied with a 75% probability in the NBA. What is the probablility any given player will make 2 consecutive shots assuming that they are independent events?

56.25%

200

A player is participating in a 3 pt. shot contest. The given probability for a 3 pt. shot is 48%. What is the probability that a player will make exactly 3 out of 5 shots?

(5c3) x .48^3 x .52^2 =29.9%

300

In a given game the probability that a specific player will make a shot is 67%. What is the probability that the player will make at least 8 of their 12 attempted shots?

1-binomcdf(12,.67,7) = 64%

400

Nate Rouse makes 3% of his halfcourt shots. What is the probability that he can make three in a row if all are independent?

(.03)^3 = .000027 (Good luck Nate)

500

A player is having a horrible game. The probability of making a 2 pt. shot in this game for this player is 23%. What is the probability that it will take no more than 5 attempts to finally make 1 shot?

geometcdf(.23,5) = 72.9%

Coaches

100

The probability that any basketball coach gets fired after each season is 38%. What is the probability that Scott Skiles does not get fired until after his fourth season?

.62 x .62 x .62 x .38 = 9.05 % OR Geometpdf(.38, 4) = 9.05 %

200

Erik Spolstra has a winning percentage of 72%. There are 82 games in an NBA season. What is the probabilityb that he wins at least 50 games this season?

1-binomcdf(82, .72, 50) = .979

300

Larry Brown has a win percentage of 48%. What is the probability that he wins exactly 7 of the next 10 games?

(10c7) * (.48)^7 * (.52)^3 = .0991 = 9.91%

400

It is expected that the probability of getting hired as an NBA coach when one applies for the job is 20%. A specific coach wants to know his chances of getting hired. Design a simulation that will approximate the percentage.

Key Component: Whether a coach is hired or not Assumptions: P(hired) = .2 P(not hired) = .8 Each hire is independent Model: Random # 1-10 1-2 = hired 3-10 = not hired Trial: Randomly generate a # 1-10 T1: 5 = no hire T2: 2 = hire T3: 8 = no hire Complete 25 - 30 trials.

500

George Karl puts 18 marbles in a bowl. Each marble has a different player's name on it. He randomly selects 5 marbles to use as his starting lineup for that night's game. His best player's marbles are larger than the others, and have a 7% chance of being selected. The other 13 marbles have a 5% chance of being selected. What is the probability that all 5 stars are chosen without replacement?

(.07/1) * (.07/.93) * (.07/.86) * (.07/.79) * (.07/.72) = .00000369