Question

On average, a basketball player makes 30% of the shots she attempts. in a typical game, she attempts 20 shots. design and carry out a simulation to determine the probability that the player will make at least 7 shots in a game.

• identify the event to be modeled: the event is the player attempting shots. there are 2 possible outcomes: _____ or _____

please help and thank you. ​

Answer 1

• shot made (probability 0.3)
• shot not made (probability 0.7)

Explanation:

In the attached spreadsheet, I elected to model each shot of each game. The model only covers 50 games, so cannot give the desired probability with much accuracy.

The cell that models the outcome of a shot has the formula ...

=IF(RAND()<=0.3;1;0)

The RAND() function in this NeoOffice spreadsheet program returns a number uniformly distributed between 0 and 1. We have elected to make numbers of 0.30 or less correspond to shots that are made. (On average, 30% of shots are made.) Each line of 20 shots models one game.

Column B adds the "Shot Successful" numbers to determine the total number of successful shots in that game. Cell B53 finds the total number of games with at least 7 shots made, and divides that number by 50 to find the probability of making 7 or more shots in a game.

I suspect one would need to model several thousand games to determine the probability with any confidence. (The probability based on the binomial distribution is about 0.392. A few different simulations (recalculating the spreadsheet) have given results ranging from 0.24 to 0.62.)